authors: bhavana bharat dalvi , meghana kshirsagar , s. sudarshan

Authors: Bhavana Bharat Dalvi, Meghana Kshirsagar, S. Sudarshan

Presented By: Aruna

Keyword Search on External Memory Data Graphs

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Outline Introduction Modeling

Graph Model 2-stage Graph Model Multi-granular Graph Representation

Algorithms Iterative Expansion Search Incremental Expansion Search

Experiments Conclusion

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Keyword Search Keyword search

A very simple and easy-to-use mechanism to get information from databases.

Keyword search queries A set of keywords.

Allows users to find interconnected tuple structures containing the given keywords in an relational database.

Combines data from multiple data sources.

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Keyword Search on Graph Data (1/2) Query result

Rooted trees that connect nodes matching the keywords.

Keyword searches – ambiguous and query results may be irrelevant to a user Ranking function

Top-k answers to keyword query.

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Keyword Search on Graph Data (2/2) Keyword search on databases Information may split across the tables/tuples due to normalization. Use of artificial documents. Use of data graphs in the absence of schema.

Graph Data Model: Lowest common denominator. Integrates data from multiple sources from different schemas. Enables novel systems for heterogeneous data integration

and search. Query result

A subtree where no node or edge can be removed without losing keyword matches.

Most of the previous work assumes graph fits in memory.

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External memory data graph (1/2) Problem with in-memory algorithms - if graph

size is more than memory.

Solutions :1. Virtual memory

Significant I/O cost Thrashing

2. SQL For relational data only Not good for top-k query answer generation

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External memory data graph (2/2) Goal of the paper:

Use a compressed graph representation to reduce IO. Graphs which are larger than memory.

Solution uses Multi-granular graph Two approaches

1. Iterative approach2. Incremental approach

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Graph Model (1/2) Nodes: Every node has an associated set of

keywords, with weights or prestige. Influences the rank of answers containing the node.

Edges: directed and weighted.

Keyword query : a set of terms ki, i=i….n.

Answer tree: a set-of-paths model, with one path per keyword. Each path (root to a node) contains the keyword.

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Graph Model (2/2) Node score : sum of the leaf/root node

weights.

Edge score of an answer: sum of the path lengths.

Answer score : a function of the node score and the edge score of the answer tree.

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Keyword Search

Steps to generate top-k answers: Looking up an inverted keyword index to get

the node-ids of nodes. Keyword nodes

Use of a graph search algorithm to find out trees connecting the keyword nodes found above. Finds rooted answer trees, which should be

generated in ranked order.

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SuperEdges

Supernode Graph

Edge weights: wt(S1 → S2): min{wt(i → j): i S1, j S2}

Source: http://www.cse.iitb.ac.in/~sudarsha/pubs.html

Clustering nodes in the full graph into supernodes, with superedges.

http://www.cse.iitb.ac.in/~sudarsha/pubs.html


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2-Phase Search (1/2) First-Attempt Algorithm:

Phase 1 : Search on supernode graph to get top-k results

(containing supernodes) Using any search algorithm

Expand all supernodes from supernode results.

Phase 2 : Search on this expanded component of graph to get

final top-k results.




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2-Phase Search (2/2)

Top-k on expanded component may not be top-k on full graph.

Experiments show poor recall.

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Multi-granular (MG) graphs (1/3) Combines a condensed version of the graph

(the “supernode graph”) Always memory resident.

Supernode graph: Clustering nodes in the full graph into supernodes,

with superedges.

All information about the part of the full graph, currently available in memory.

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Multi-granular (MG) graphs (2/3)

Node numbering scheme = supernode.innernode

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Multi-granular (MG) graphs (3/3) Edge-weights:

S1 S2: Min {edge-weight n1 n2 | n1 S1 and n2 S2}

S i : Min {edge-weight s i | s S}

I I: Edge weight is same as in original graph.

Supernode answer: Answer containing supernodes if we execute search on

the MG graph.

Pure answer: Answer that does not contain any supernodes.

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Iterative Expansion Search (1/3) Input : a MG graph.

Output : top k pure results.

Iterative search on MG graph Repeat

Search on current MG graph using any search algorithm, to find top results.

Expand super nodes in top results. Until top k answers are all pure.

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Iterative Expansion Search (2/3)

Yes

Output

No

Expand supernodes in top answers

Edges in top-k answers

Explore (generate top-k answers on current MG graph, using any in-memory search method)

top-k answers pure?




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Iterative Expansion Search (3/3) Guarantees finding top- k answers

Very good IO efficiency compared to search using virtual memory.

Nodes expanded above never evicted from “virtual memory” cache. Expanded nodes retain in logical MG graph, re-

fetch as required. Can cause thrashing.

But high CPU cost due to repeated work.

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Incremental Expansion Search Motivation :

Repeated restarts of search in iterative search.

Basic idea: Search on MG graph Expand supernode(s) in top answer. Unlike iterative search

Update the state of the search algorithm when a supernode is expanded, and

Continue search instead of restarting. Run search algorithm until top k answers are all pure.

State update depends on search algorithm. Use of backward expanding search.




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Backward Expanding Search Based on Dijkstra’s single-source shortest path algorithm. One shortest path search iterator per keyword. Runs n copies of this algorithm concurrently.

Explored nodes: nodes for which shortest path already found.

Fringe nodes: unexplored nodes adjacent to explored nodes.

SPI tree: shortest path iterator tree Tree containing explored and fringe nodes. Edge uv if (current) shortest path from u to keyword passes through v.

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Incremental backward search Backward search run on multi-granular graph

Algorithm: Repeat

Find next best answer on current multi-granular graph.

If answer has supernodes Expand supernode(s)

Update the state of backward search, i.e. all SPI trees, to reflect state change of multi-granular graph due to expansion

Until top-k answers on current multi-granular graph are “pure” answers




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Incremental Search (1/3)

SPI tree for k1




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1. Affected nodes get detached.

2. Inner-nodes get attached (as fringe nodes) to adjacent explored nodes based on shortest path to K1.

3. Affected nodes get attached (as fringe nodes) to adjacent explored nodes based on shortest path to K1.

State Update on Supernode Expansion

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Effects of supernode expansion Differences from Dijkstra's shortest-path algorithm:

For Explored nodes: Path-costs of explored nodes may increase. Explored nodes may become fringe nodes.

For Fringe nodes: Incremental Expansion: Path-costs may increase or

decrease.

Invariant SPI trees reflect shortest paths for explored nodes in

current multi-granular graph.

Theorem: Incremental backward expanding search generates correct top-k answers.

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Heuristics Thrashing Control :

Stop supernode expansion on cache full. Use only parts of the graph already expanded for

further search.

Intra-supernode edge weight

Heuristics can affect recall Recall at or close to 100% for relevant answers,

with heuristics, in the experiments.

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Experimental Setup Clustering algorithm to create supernodes

Experiments use Edge prioritized BFS. Ongoing work: develop better clustering

techniques

All experiments done on cold cacheDataset Original

Graph SizeSupernode Graph Size

Edges Superedges

DBLP 99MB 17MB 8.5M 1.4M

IMDB 94MB 33MB 8M 2.8M

Default Cache size (Incr/Iter) 1024 (7MB)Default Cache Size (VM, DBLP) 3510 (24MB)

Default Cache Size (VM, IMDB) 5851 (40MB)




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External memory search: performance Supernode graph very effective at minimizing IO

Cache misses with incremental often less than no. of nodes matching keywords.

Iterative algorithm High CPU cost.

VM (backward search with cache as virtual memory) has high IO cost. Use same clustering as for supernode graph. Fetch cluster into cache whenever a node is accessed.

Evicting LRU cluster if required. Search code unaware of clustering/caching.

Gets “Virtual Memory” view.

Incremental combines low IO cost with low CPU cost.

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Query Execution Time (top 10 results)




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Cache Misses for Different Cache Sizes

All Incr.

All VM




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Query Execution Time (Last Relevant Result)




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Conclusions Graph summarization coupled with a multi-

granular graph representation shows promise for external memory graph search.

Ongoing/Future work Applications in distributed memory graph search. Improved clustering techniques. Extending Incremental to bidirectional search and

other graph search algorithms. Testing on really large graphs.

authors: bhavana bharat dalvi , meghana kshirsagar , s. sudarshan

Documents

keyword query

keyword nodes

graph data model

graph search algorithm

aruna keyword search

keyword searchsteps

keyword matches

graph size