Associative Peer to Peer Networks: Harnessing Latent Semantics

1. Associative Peer to Peer Networks: Harnessing Latent Semantics Edith Cohen AT&T Labs-research Amos Fiat Haim Kaplan Tel-Aviv University Stanford Networking Seminar

2. Web server “Traditional” Client-server Web Stanford Networking Seminar

3. Peer-to-peer Networks Distributed network for sharing content (music, video, software, etc.), where each host acts as both a server and a client • Harness vast resources • Scalability/Robustness to failures/shutdowns Stanford Networking Seminar

4. P2P Search Overall performance of a P2P network highly depends on the efficiency and versatility of search • Scope: ability to locate “rare” items “Find the 10th episode of Star Trek Voyager” • Partial-match/complex queries: “Find an Indiana Jones movie” …Or “Indiana Joens” movie….. What features are important ? Stanford Networking Seminar

5. Blind Search(Gnutella, FastTrack – Morpheus/ Kazza,…): search via flooding, multi-head random walks... • Distributed Hash Tables (Freenet, Can, Chord,…):induced topology routed search. (search in) Basic P2P Architectures Partial-Matches Decentralized: peers are connected by low-degree overlay network. Scope Centralized(Napster): central index service. Stanford Networking Seminar

6. Associative P2P networks Retain Gnutella’s desirable properties: • Distributed overlay network • Peers store only what they need (“common good” at par with “own welfare”) • No tight control of topology/content • Support partial-match queries AND • Have search scope (orders of magnitude improvement over Gnutella) • Make implicit use of latent semantics • Provably good on a reasonable model • Very good on simulations Stanford Networking Seminar

7. P2P search framework • Search queries are propagated on the overlay (from peer to a neighbor peer). • When a peer receives a query, it checks if it can satisfy it; decreases hop count; and forwards it to a subset of its neighbors. • Each search includes query and a “propagation rule”, which determines which neighbors the search is propagated to. “DHTs” propagation rule= hash of query “Gnutella” propagation rule independent of query Associative propagation rules are predicates (guide rules) Stanford Networking Seminar

8. Overview • What do we mean by “latent semantics” ? • Challenges in using latent semantics in P2P setting • Our proposal: search propagation via Possession rules • Possession rules overlays • Search strategies • Possession rules search strategies: Rapier, GAS • Models for “blind search” strategies (gnutella) • Analysis in the Itemsets model • Experimental evaluation • More on GAS search strategy Stanford Networking Seminar

9. View of P2P file sharing network Stanford Networking Seminar

10. What is latent semantics? • Selections people make are dependent: • If you buy baby formula, you are more likely to buy diapers. • If two people loved a show, they are more likely to agree on other shows. • Peer/Item matrix is “Market Basket” dataset. Similar to buyers/items, Document/terms, Web-pages/hyperlinks, movies/viewers. • Applications for extracting patterns from market basket data: Information Retrieval, Collaborative Filtering, Web search, Marketing, Recommendation Systems,…. (clustering, search, association rules) ?? P2P search – direct queries to peers with interests that match yours Stanford Networking Seminar

11. Challenges • Overlay topology (“networking aspects”) must be coupled with search strategy (“Information Retrieval/Data-Mining”) • “Traditional” IR and data-mining tools are not adapted to the highly distributed P2P setting. • Similarity metrics/clustering/ranking involve matrix operations on the “market basket” data: principal component analysis (LSI), eigenvalue computations, association rules… Stanford Networking Seminar

12. “Network”: How to build overlay that supports possession rules • “IR/DM”: design search strategies that use possession rules (and work!) Possession Rules • Rule(O): do you possess item O ? • Peer maintains a possession rule for each item in its index (subset if index is large) • Search strategy: a sequence of possession rules (with “hop counts”/search size limit) Making this work: Stanford Networking Seminar

13. Example Search Strategy of P26: 2 hops in rule(A) 4 hops in rule(B) 6 hops in rule(C ) 4 hops in rule(A) 3 hops in rule(D) Possession-rules overlays Peer26 Index of P26 Rules/Items: Rule(A) Rule(B) Rule(C ) Rule(D) Stanford Networking Seminar

14. Blind searching for O takes 13 probes Searching with rule(O) takes 2 probes Rules/Items: Rule(A) Rule(B) Rule(C ) Rule(D) Stanford Networking Seminar

15. Possession-rule overlay Network is “gnutella-like”, within each rule • Coverage: The induced overlay on peers that satisfy each rule constitutes of large connected components. • Small degree: Each peer participates in a limited number of rules. (yet, overall there is a large number rules), for each rule it “participates” in, the peer maintains several participating neighbors. • Overlay and search boost each other (easy to find appropriate neighbors for each rule): • When you find O, you often discover multiple peers that have O; when you give O, the searcher informs you of other peers with O. • Peers that have O can find other peers that have O (… can use “super-peer” overlay within each rule !!) Stanford Networking Seminar

16. Search strategies • To beat blind search, associative search should probe peers that are more likely to answer than “random peers” Associative search: • RAPIER: Random Possession Rule – crudest strategy • GAS: Greedy Selection – refined strategy • Blind search: • Urand: (“gnutella”) all peers have same likelihood of being probed in each query • Prand: (“gnutella modified”) peers are probed proportionally to their index size (RAPIER has same bias) Stanford Networking Seminar

17. RAPIER – Random Possession Rulesimplest possession-rule based strategy RAPIER Search strategy: • Repeat until found: • Pick a random item O from your index • Search peers that have this item (using rule(O)) Straightforward to implement on top of a possession-rule overlay network Stanford Networking Seminar

18. Analysis: Itemsets Model • Items belong to “topics.” There are very many topics; but each peer can only select items from a fixed set of topics. Topic popularities can highly vary; but each peer has equal interest in each of “its” topics. We show that • RAPIER is at least as good as Prand • RAPIER is better than Prand when peers have fewer topics Simple model that hints on what is going on… Stanford Networking Seminar

19. Experiments Data: used Client/Hostname matrix from proxy logs as peer/item matrix. Each entry, in turn, is treated as a search item. • Similarly-structured “market basket” data • Has rare items (which current P2P networks don’t support) • No universal model for market basket data • Can’t get a full index for many peers from current P2P networks… and these networks don’t reflect well on rare items. • Metric: ESS (Expected Search Size – number of peers probed till search is resolved). CDF of fraction of “searches” that have ESS below “x”. Stanford Networking Seminar

20. ESS – Expected Search Size • ESS: 1/(success probability in each probe) (when probes are “independent” – not true for GAS) • Probe success probability: • Urand: fraction of peers that have the item in their index • Prand: weight of each peer is its index size divided by sum of index sizes of all peers. • Success prob: (weight of peers with item) / (weight of peers without item) • RAPIER: the average, over possession rules peer participates in, of fraction of peers in rule that have the item. Stanford Networking Seminar

21. Peer-Item Matrix - Experiment Items ? ? ? ? ? ? Peers ? ? Stanford Networking Seminar

22. Urand Ps=3/9 ESS=3 Prand ESS=29/9 1/9 3/29 3/29 1/9 1/9 3/29 1/9 3/29 3/29 1/9 1/9 5/29 1/9 3/29 1/9 3/29 1/9 3/29 Urand and Prand Items Peers ? Stanford Networking Seminar

23. rule rule 0.5 0.5 0.5 0.25 0.25 RAPIER (Random Possession Rule) Items Peers ? Stanford Networking Seminar

24. Caveat: comparing apples and oranges • When searching by possession rules we have bias towards peers that participate in more rules/ have more items. • But, with this bias, a strategy has better chance of finding what it is looking for! So… • We show that the likelihood of being probed is proportional to number of rules you participate in. • Prand “blind search” strategy has same bias. • Thus, it is “fair” to compare Prand search with possession-rule based RAPIER Stanford Networking Seminar

25. GAS – Greedy Strategy GAS …Refining RAPIER Ideas: • Some rules are better than others (e.g., possession of a very popular item carries weaker information) • Unsuccessful search carries information: suppose you lost something, you think you lost it at home. You search home going through various closets and drawers and don’t find it, then you may decide to go search the office, even if you have not completed an exhaustive search at home. What happened? The posterior distribution on the item’s location had changed as a result of the search. Stanford Networking Seminar

26. All Items Urand Blind search (Gnutella), Prand Gnutella modified, Rapier, GAS – our algorithms Stanford Networking Seminar

27. Rare Items: present in 1% of peers Stanford Networking Seminar

28. Rarer items: 0.1% of peers Stanford Networking Seminar

29. Even Rarer Item: 0.01% of peers Stanford Networking Seminar

30. GAS – Greedy Strategy • Idea: use the search strategy that would have optimized your search on previous queries. • Caveat: this is NP-Complete • Can do: greedy approximation strategy: GAS GAS: • initialize the “query vector” to a uniform distribution on previous selections. • Iterate the following: • Apply the possession rule that maximizes success probability with respect to the query posterior • update the query posterior. Theorem: GAS is a constant factor approximation of the optimal strategy Stanford Networking Seminar

31. Building GAS strategies • GAS: • Take a sample of items currently in your index D,E,F,G. • “search” for these items in each possession rule you participate A,B,C • obtain a matrix: fraction of peers with item x in rule(y) Stanford Networking Seminar

32. GAS strategy (example) C,C,C,A,C,C,A,C,A,C,B,B,A,C,B,B,C,A,B,B,C GAS search of size 21: 10 probes in rule(C) 6 probes in rule(B) 5 probes in rule(A) RAPIER search of size 21: 7 probes in rule(C) 7 probes in rule(B) 7 probes in rule(A) Stanford Networking Seminar

33. Summary • We proposed a general framework for associative P2P search: exploit patterns inherent in human selections to boost search. Adapted to the P2P setting. • Search strategies and the overlay structure are “symbiotic” and guided/boosted by previous selections/queries. • “Common good” in par with “own welfare”: All data maintained by each peer has direct personal benefit (like gnutella). Helping others helps you… • Possession rules: • Strategies are “approximations” to “standard” similarity metrics… that work!!. • Easy to find other sources of desired item (for alternative/parallel downloads) Stanford Networking Seminar

34. Related work • IR-DM: association rules/collaborative filtering/Web search • P2P networks: unstructured networks; DHTs • DHTs have “symbiotic” overlay/search strategy • Caching at peers (Freenet) adapt overlay according to search • Intersection: • Crespo/Garcia-Molina 02– routing indexes System isolates “topics”+map queries/items to topics. Peer knows “summary” of what can be reached thru it/each neighbor Query keywords are used to select a neighbor who is a best match Differences from our approach: • No connection between search and overlay topology • Uses only text/keywords. We use co-location associations between items. CG02: tradeoff between topic divergence (all nodes ending up with similar index “summary”); or restricted coverage (number of peers included in each peer summary); • neurogrid.net (Sam Joseph, U. Tokyo) “agent” text-based approach • Peers learn and remember content of other peers Stanford Networking Seminar

35. Future… • Integrate text matching (of query keywords) in search strategy (use rule(O) if query keywords match O’s metadata) • Select which possession rules to participate in (e.g., using item popularity heuristic or GAS-like selection) • Search strategy gives more weight to more recent selections (are more indicative of next query) • Explore other types of propagation rules • P2P “communities” ? • Integrate “Recommendation Systems” in P2P ? • Implementation … Stanford Networking Seminar

36. Thank You! Stanford Networking Seminar

37. Some Extra Comments… • Issues with straightforward importing of IR techniques • Vector space approach • Similarity metrics • Why we need to use several propagation rules in a search? (when searching according to “examples” in the index) Stanford Networking Seminar

38. “Straight” IR vector-space approach • Peers are mapped to vectors, according to their index content. Queries are mapped to the vectors in the same space. • Overlay topology is correlated with distances in this vector space (bias towards closer peers) • Search propagation targets regions of the space that are “closest” to the query. • #neighbors=O(dimension) - want small dimension • Yet, Matrix operations, e.g principal component analysis (LSI), are hard in our distributed setting • Yet, each peer should be able to compute the mapping for its queries and/or index • Proximity metric alone is insufficient (Need different propagation rules) Stanford Networking Seminar

39. Why we need several propagation rules for the same query –”decision-tree like” search propagation rule =approx interest area Each peer covers several interest areas, peers have different sets of interest areas. Peer Query: 80% basketball 20%polo “World” Index: 5% basketball 0.1% polo All “basketball” lovers would be close matches; but need to direct search to more “polo” lovers multi-rule search strategy: “basketball” 200 peers; “polo” 200 peers Stanford Networking Seminar