Social content matching in MapReduce Gianmarco De Francisci Morales Aristides Gionis Mauro Sozio 10 March 2011 

Outline Application scenario Problem statement Algorithms Experimental evaluation Conclusions 

Social Media 

Social Media 

Social Media 

Social Media 

A needle in a haystack User generated content Users are both consumers and producers Large volume Diverse Difficult to navigate Difficult to find interesting things 

Featured Item Be proactive! Propose content to users (interesting photos, open questions, etc..) Increase the engagement of the user with the platform Effectiveness of the system depends on: Relevance (consumer) Exposure (producer) 

Graph b-matching Given a set of items T, consumers C, bipartite graph, weights w(ti, cj), capacity constraints b(ti) and b(cj) The goal is to find a matching M = {(t, c)} such that: (i) |M(ti )| ≤ b(ti ) (ii) |M(cj )| ≤ b(cj ) (iii) the total value w(M) of the matching is maximized 

Graph b-matching Items Consumers 

Graph b-matching Items Consumers 

Graph b-matching Items Consumers 

Contributions Investigate the b-matching problem in the context of social content distribution Devise a fully-MapReduce framework to address it StackMR GreedyMR Use SSJ-2R to build the graph Large scale experiments with real-world datasets 

System overview The application operates in consecutive phases (each phase in the range from hours to days) Before the beginning of the ith phase, the application makes a tentative allocation of items to users Capacity constraints User: an estimate of the number of logins during the ith phase Items: proportional to a quality assessment or constant B = c∈C b(c) = t∈T b(t) 

Graph building Edge weight is the cosine similarity between some vector representations of the item and the consumer w(ti, cj) = v(ti ) · v(cj) Prune the candidate edges O(|T||C|) by discarding low weight edges (we want to maximize the total weight) Similarity join between T and C in MapReduce 

StackMR Primal-dual formulation of the problem (Integer Linear Programming) Compute a maximal ⌈㸜C⌉-matching in parallel Push it in the stack, update dual variables and remove covered edges When there are no more edges, pop the whole stack and include edges in the solution layer by layer For efficiency, allows (1+∊) violations on capacity constraints 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

StackMR Example 

GreedyMR Adaptation in MR of a classical greedy algorithm (sort the edges by weight, include the current edge if it maintains the constraints and update the capacities) At each round, each node proposes its top weighting b(v) edges to its neighbors The intersection between the proposal of each node and the ones of its neighbors is included in the solution Capacities are updated in parallel Yields a feasible sub-optimal solution at each round 

StackGreedyMR Hybrid approach Same structure as StackMR Uses a greedy heuristic in one of the randomized phases, when choosing the edges to propose We tried also with a proportional heuristic, but the results were always worse than with the greedy one Mixed results overall 

Algorithms summary Approximation guarantee MR rounds Capacity violations StackMR GreedyMR ⅙ poly- logarithmic 1+∊ ½ linear no 

Datasets 3 datasets: flickr-small, flickr-large, yahoo-answers user capacities: α-proportional to user activity item capacities: proportional to #favorites for flickr, constant for Yahoo! answers weight threshold σ to sparsify the graph Dataset |T| |C| |E| flickr-small 2 817 526 550 667 flickr-large 373 373 32 707 1 995 123 827 yahoo-answers 4 852 689 1 149 714 18 847 281 236 b(u) = α n(u) b(p) = f(p) u αn(u) q f(q) b(q) = u αn(u) |Q| 

Vector representation Bag-of-words model flickr users: set of tags used in all photos flickr items (photos): set of tags Y! Answers users: set of words used in all answers Y! Answers items (questions): set of words Y! Answers: stopword removal, stemming, tf-idf 

Measures Quality = b-matching value Efficiency = number of MR rounds Evaluation of capacity violations for StackMR Evaluation of convergence speed for GreedyMR Parameter exploration for α and σ 

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Conclusions 2 algorithms with different trade offs between result quality and efficiency StackMR scales to very large datasets, has provable poly-logarithmic complexity and is faster in practice, capacity violations are negligible GreedyMR yields higher quality results, has ½ approximation and can be stopped at any time 

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