a brief history and recent achievements ... - computer...
TRANSCRIPT
![Page 1: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/1.jpg)
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
A Brief History and Recent Achievements in
Bidirectional SearchNathan R. Sturtevant, University of Denver
Ariel Felner, Ben Gurion University
Other major contributors:Jingwei Chen, University of Denver
Eshed Shaham, Ben Gurion UniversityRobert Holte, University of AlbertaSandra Zilles, University of Regina
![Page 2: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/2.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Key Related Work• 1959 - Dijkstra’s Algorithm
2
![Page 3: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/3.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Key Related Work• 1959 - Dijkstra’s Algorithm• 1966 - Bidirectional Search (Nicholson & Doran)
2
![Page 4: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/4.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Key Related Work• 1959 - Dijkstra’s Algorithm• 1966 - Bidirectional Search (Nicholson & Doran)• 1968 - Heuristic Search (Hart, Nilsson & Raphael)
2
![Page 5: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/5.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Key Related Work• 1959 - Dijkstra’s Algorithm• 1966 - Bidirectional Search (Nicholson & Doran)• 1968 - Heuristic Search (Hart, Nilsson & Raphael)• 1969 - Bidirectional Heuristic Search (Pohl)
2
![Page 6: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/6.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Key Related Work• 1959 - Dijkstra’s Algorithm• 1966 - Bidirectional Search (Nicholson & Doran)• 1968 - Heuristic Search (Hart, Nilsson & Raphael)• 1969 - Bidirectional Heuristic Search (Pohl)• 1985 - A* Theory (Dechter & Pearl)
3
![Page 7: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/7.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Overview• Bidirectional Theory
• Eckerle et al, ICAPS 2017• Optimal algorithm (offline)
• Shaham et al, SoCS 2017• Near-optimal algorithm (online)
• Chen et al, IJCAI 2017
4
![Page 8: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/8.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Assumptions• Front-to-end bidirectional search• Admissible algorithms
• Performance with consistent heuristics• Deterministic, black box algorithm
5
![Page 9: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/9.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Unidirectional Theory• ANY admissible unidirectional search algorithm:
• Must expand ALL states with:• f(s) = g(s) + h(s) < C*
• Otherwise we can construct instances on which it won’t find the optimal solution
6
![Page 10: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/10.jpg)
What states must be expanded by all
bidirectional algorithms?
![Page 11: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/11.jpg)
![Page 12: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/12.jpg)
![Page 13: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/13.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Conclusion• Given a single state s
• There exists a bidirectional algorithm that does not expand s
9
![Page 14: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/14.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Conclusion• Given a single state s
• There exists a bidirectional algorithm that does not expand s
• Given some pairs of states (u, v)• We can avoid expanding u• We can avoid expanding v• We can’t avoid expanding BOTH u and v
9
![Page 15: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/15.jpg)
High-Level Picture
startgoal
![Page 16: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/16.jpg)
High-Level Picture
startgoal
u v
![Page 17: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/17.jpg)
High-Level Picture
startgoal
u v
![Page 18: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/18.jpg)
High-Level Picture
startgoal
u v
![Page 19: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/19.jpg)
High-Level Picture
startgoal
u vgF(u)
![Page 20: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/20.jpg)
High-Level Picture
startgoal
u vgF(u)
h(u, goal)
![Page 21: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/21.jpg)
High-Level Picture
startgoal
u vgF(u)
h(u, goal)
fF(u) = gF(u) + h(u, goal)
![Page 22: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/22.jpg)
High-Level Picture
startgoal
u v
![Page 23: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/23.jpg)
High-Level Picture
startgoal
u vgB(v)
![Page 24: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/24.jpg)
High-Level Picture
startgoal
u vgB(v)
h(start, v)
![Page 25: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/25.jpg)
High-Level Picture
startgoal
u vgB(v)
h(start, v)
fB(v) = gB(v) + h(start, v)
![Page 26: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/26.jpg)
High-Level Picture
startgoal
u v
![Page 27: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/27.jpg)
High-Level Picture
startgoal
u vgF(u)
![Page 28: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/28.jpg)
High-Level Picture
startgoal
u vgF(u)
gB(v)
![Page 29: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/29.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Theorem
• If lb(u, v) < C* then we must expand either u or v• Leads implicitly to termination conditions
14
lb(u, v) = max(fF (u),
fB(v),
gF (u) + gB(v))
Sufficient Conditions for Node Expansion in Bidirectional Heuristic Search, Jurgen Eckerle, Jingwei Chen, Nathan Sturtevant, Sandra Zilles and Robert Holte, International Conference on Automated Planning and Scheduling (ICAPS), 2017
f-cost:estimate of total
path length
![Page 30: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/30.jpg)
![Page 31: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/31.jpg)
fF (u) < C⇤
![Page 32: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/32.jpg)
fB(v) < C⇤
![Page 33: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/33.jpg)
![Page 34: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/34.jpg)
gF (u) + gB(v) < C⇤
![Page 35: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/35.jpg)
gF (u) + gB(v) < C⇤
![Page 36: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/36.jpg)
0
1
1
2
3
2
3
4.5
4
6
5.5
7.5
7
8.5
0
1
2
2.5
2
3.5
4
3
3.5
3
5.5
4.5
5
6.5
5.5
6
7.5
6.5
7
4
5
6
4.5
5.5
8.5
gF (u) + gB(v) < C⇤
![Page 37: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/37.jpg)
0
1
1
2
3
2
3
4.5
4
6
5.5
7.5
7
8.5
0
1
2
2.5
2
3.5
4
3
3.5
3
5.5
4.5
5
6.5
5.5
6
7.5
6.5
7
4
5
6
4.5
5.5
8.5
gF (u) + gB(v) < C⇤
C* = 10.5
![Page 38: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/38.jpg)
0
1
1
2
3
2
3
4.5
4
6
5.5
7.5
7
8.5
0
1
2
2.5
2
3.5
4
3
3.5
3
5.5
4.5
5
6.5
5.5
6
7.5
6.5
7
4
5
6
4.5
5.5
8.5
gF (u) + gB(v) < C⇤
C* = 10.5
![Page 39: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/39.jpg)
0
1
1
2
3
2
3
4.5
4
6
5.5
7.5
7
8.5
0
1
2
2.5
2
3.5
4
3
3.5
3
5.5
4.5
5
6.5
5.5
6
7.5
6.5
7
4
5
6
4.5
5.5
8.5
gF (u) + gB(v) < C⇤
C* = 10.5
GMX
![Page 40: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/40.jpg)
gF (u) + gB(v) < C⇤
![Page 41: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/41.jpg)
gF (u) + gB(v) < C⇤
![Page 42: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/42.jpg)
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 43: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/43.jpg)
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 44: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/44.jpg)
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
C* = 10.5
![Page 45: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/45.jpg)
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
C* = 10.5
![Page 46: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/46.jpg)
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
C* = 10.5
![Page 47: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/47.jpg)
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
Total Work: 25
C* = 10.5
![Page 48: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/48.jpg)
Total Work: 27
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 49: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/49.jpg)
Total Work: 28
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 50: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/50.jpg)
Total Work: 27
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 51: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/51.jpg)
Total Work: 26
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 52: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/52.jpg)
Total Work: 22
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 53: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/53.jpg)
Total Work: 21
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 54: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/54.jpg)
Total Work: 18
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 55: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/55.jpg)
Total Work: 17
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 56: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/56.jpg)
Total Work: 15
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 57: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/57.jpg)
Total Work: 14
C* = 10.5
01
12 12
22
32
22
32
4.51
41
61
5.51
7.51
71
8.51
0 1
1 1
2 2
2.5 1
2 2
3.5 2
4 2
3 2
3.5 2
3 2
5.5 3
4.5 2
5 2
6.5 2
5.5 3
6 2
7.5 1
6.5 2
7 1
4 2
5 2
6 2
4.5 2
5.5 3
8.5 1
![Page 58: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/58.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
![Page 59: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/59.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
Forward
![Page 60: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/60.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
ForwardBackward
![Page 61: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/61.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
ForwardBackward
![Page 62: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/62.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
ForwardBackward
![Page 63: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/63.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
ForwardBackward
![Page 64: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/64.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
ForwardBackward
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
![Page 65: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/65.jpg)
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path LengthStart Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
ForwardBackward
Start Goal
Nod
e Ex
pans
ions
0
100k
200k
300k
Path Length
![Page 66: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/66.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Fractional MM• Takes a parameter ƒ
• Cost of the state space to explore in each direction• Costs correspond to different vertex covers
• We can (offline) compute the best algorithm for a given search problem
37
The Minimal Set of States that Must be Expanded in a Front-to-end Bidirectional Search, Eshed Shaham, Ariel Felner, Jingwei Chen and Nathan R. Sturtevant, Symposium on Combinatorial Search (SoCS), 2017
![Page 67: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/67.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE Vertex Cover on
a Bipartite Graph• Approximation algorithm:
• Repeat until all vertices covered• Choose any edge/line with uncovered vertex• Place both states into vertex cover
• Gives 2x approximation to optimal vertex cover• (Papadimitriou & Steiglitz, 1982)
38
![Page 68: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/68.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
39
![Page 69: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/69.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go
39
![Page 70: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/70.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go• We don’t know the optimal solution cost
39
![Page 71: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/71.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go• We don’t know the optimal solution cost
• Must estimate C*
39
![Page 72: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/72.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go• We don’t know the optimal solution cost
• Must estimate C*• We must avoid re-expanding states
39
![Page 73: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/73.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go• We don’t know the optimal solution cost
• Must estimate C*• We must avoid re-expanding states
• Carefully order state expansions
39
![Page 74: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/74.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go• We don’t know the optimal solution cost
• Must estimate C*• We must avoid re-expanding states
• Carefully order state expansions• Computing lb(u, v) could be expensive
39
![Page 75: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/75.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Using this algorithm• We don’t know the full graph ahead of time
• Build the graph as we go• We don’t know the optimal solution cost
• Must estimate C*• We must avoid re-expanding states
• Carefully order state expansions• Computing lb(u, v) could be expensive
• Efficient data structures
39
![Page 76: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/76.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
NBS• Put start/goal onto forward/backward priority queues• While forward/backward not empty
• Among all state on queues:• Select the pair with lowest lb• Expand both of them
• Terminate when lb ≥ best path• Gives 2x bound on optimal number of expansions
• Bound is tight
40
Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017
![Page 77: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/77.jpg)
NBS A*
![Page 78: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/78.jpg)
NBS A*
![Page 79: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/79.jpg)
Instancey=xy=2xy=x/2
Nec
essa
ry E
xpan
sion
s by
NB
S
0
5k
10k
15k
20k
Necessary Expansions by A*0 10k 20k
Necessary Node Expansions (brc203d)
![Page 80: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/80.jpg)
Instancey=xy=2xy=x/2
Nec
essa
ry E
xpan
sion
s by
NB
S
10k
100k
1M
10M
100M
Necessary Expansions by A*10k 100k 1M 10M 100M
Total Node Expansions (15 puzzle)
![Page 81: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/81.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Summary• Theory
• First definition of necessary node expansions• fMM - implements optimal bidirectional search
• Practice• Near-optimal approach (NBS)• Node expansions are bounded by 2x optimal
• Demos & videos will appear at:• https://www.movingai.com
44
![Page 82: A Brief History and Recent Achievements ... - Computer Sciencesturtevant/papers/sturtevant18smtslides.pdf · ENGINEERING & COMPUTER SCIENCE A Brief History and Recent Achievements](https://reader033.vdocuments.site/reader033/viewer/2022050608/5faf55713f6edb61391d9ca6/html5/thumbnails/82.jpg)
A Brief History and Recent Achievements in Bidirectional Search
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Open Questions• What can we learn about bidirectional search from
the minimum vertex cover?
• Is there an algorithm with better average performance?
• Efficient front-to-front search?
45