Vahab Mirrokni

Bio: Vahab Mirrokni is an academic researcher from Google. The author has contributed to research in topics: Common value auction & Approximation algorithm. The author has an hindex of 57, co-authored 346 publications receiving 14255 citations. Previous affiliations of Vahab Mirrokni include Vassar College & Microsoft.

Locality-sensitive hashing scheme based on p-stable distributions

Abstract: We present a novel Locality-Sensitive Hashing scheme for the Approximate Nearest Neighbor Problem under lp norm, based on p-stable distributions.Our scheme improves the running time of the earlier algorithm for the case of the lp norm. It also yields the first known provably efficient approximate NN algorithm for the case p

Maximizing Non-monotone Submodular Functions

Abstract: Submodular maximization generalizes many important problems including Max Cut in directed and undirected graphs and hypergraphs, certain constraint satisfaction problems, and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NP-hard. In this paper, we design the first constant-factor approximation algorithms for maximizing nonnegative (non-monotone) submodular functions. In particular, we give a deterministic local-search $\frac{1}{3}$-approximation and a randomized $\frac{2}{5}$-approximation algorithm for maximizing nonnegative submodular functions. We also show that a uniformly random set gives a $\frac{1}{4}$-approximation. For symmetric submodular functions, we show that a random set gives a $\frac{1}{2}$-approximation, which can also be achieved by deterministic local search. These algorithms work in the value oracle model, where the submodular function is accessible through a black box returning $f(S)$ for a given set $S$. We show that in this model, a $(\frac{1}{2}+\epsilon)$-approximation for symmetric submodular functions would require an exponential number of queries for any fixed $\epsilon>0$. In the model where $f$ is given explicitly (as a sum of nonnegative submodular functions, each depending only on a constant number of elements), we prove NP-hardness of $(\frac{5}{6}+\epsilon)$-approximation in the symmetric case and NP-hardness of $(\frac{3}{4}+\epsilon)$-approximation in the general case.

Optimal marketing strategies over social networks

Abstract: We discuss the use of social networks in implementing viral marketing strategies. While influence maximization has been studied in this context (see Chapter 24 of [10]), we study revenue maximization, arguably, a more natural objective. In our model, a buyer's decision to buy an item is influenced by the set of other buyers that own the item and the price at which the item is offered.We focus on algorithmic question of finding revenue maximizing marketing strategies. When the buyers are completely symmetric, we can find the optimal marketing strategy in polynomial time. In the general case, motivated by hardness results, we investigate approximation algorithms for this problem. We identify a family of strategies called influence-and-exploit strategies that are based on the following idea: Initially influence the population by giving the item for free to carefully a chosen set of buyers. Then extract revenue from the remaining buyers using a 'greedy' pricing strategy. We first argue why such strategies are reasonable and then show how to use recently developed set-function maximization techniques to find the right set of buyers to influence.

Online Stochastic Matching: Beating 1-1/e

Abstract: We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio of $1-{1\over e} \simeq 0.632$, a very familiar bound that holds for many online problems; further, the bound is tight in this case. In the online, stochastic case when nodes are drawn repeatedly from a known distribution, the greedy algorithm matches this approximation ratio, but still, no algorithm is known that beats the $1 - {1\over e}$ bound.Our main result is a $0.67$-approximation online algorithm for stochastic bipartite matching, breaking this $1 - {1\over e}$ barrier. Furthermore, we show that no online algorithm can produce a $1-\epsilon$ approximation for an arbitrarily small $\epsilon$ for this problem. Our algorithms are based on computing an optimal offline solution to the expected instance, and using this solution as a guideline in the process of online allocation. We employ a novel application of the idea of the power of two choices from load balancing: we compute two disjoint solutions to the expected instance, and use both of them in the online algorithm in a prescribed preference order. To identify these two disjoint solutions, we solve a max flow problem in a boosted flow graph, and then carefully decompose this maximum flow to two edge-disjoint (near-) matchings. In addition to guiding the online decision making, these two offline solutions are used to characterize an upper bound for the optimum in any scenario. This is done by identifying a cut whose value we can bound under the arrival distribution. At the end, we discuss extensions of our results to more general bipartite allocations that are important in a display ad application.

Trust-based recommendation systems: an axiomatic approach

Abstract: High-quality, personalized recommendations are a key feature in many online systems. Since these systems often have explicit knowledge of social network structures, the recommendations may incorporate this information. This paper focuses on networks that represent trust and recommendation systems that incorporate these trust relationships. The goal of a trust-based recommendation system is to generate personalized recommendations by aggregating the opinions of other users in the trust network.In analogy to prior work on voting and ranking systems, we use the axiomatic approach from the theory of social choice. We develop a set of five natural axioms that a trust-based recommendation system might be expected to satisfy. Then, we show that no system can simultaneously satisfy all the axioms. However, for any subset of four of the five axioms we exhibit a recommendation system that satisfies those axioms. Next we consider various ways of weakening the axioms, one of which leads to a unique recommendation system based on random walks. We consider other recommendation systems, including systems based on personalized PageRank, majority of majorities, and minimum cuts, and search for alternative axiomatizations that uniquely characterize these systems.Finally, we determine which of these systems are incentive compatible, meaning that groups of agents interested in manipulating recommendations can not induce others to share their opinion by lying about their votes or modifying their trust links. This is an important property for systems deployed in a monetized environment.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Maximizing the Spread of Influence through a Social Network

Abstract: Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.