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We consider the online bipartite matching problem in the unknown distribution input model. We show that the Ranking algorithm of [KVV90] achieves a competitive ratio of at least 0.653. This is the first analysis to show an algorithm which breaks the natural 1 - 1/e -barrier' in the unknown distribution model (our analysis in fact works in the stricter,… (More)

Applications in complex systems such as the Internet have spawned a recent interest in studying situations involving multiple agents with their individual cost or utility functions. In this paper, we introduce an algorithmic framework for studying combinatorial optimization problems in the presence of multiple agents with submodular cost functions. We study… (More)

—Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of vertices to determine if they are adjacent. If the queried edge exists, we are committed to match the two endpoints.… (More)

We consider the following stochastic optimization problem first introduced by Chen et al. in [6]. We are given a vertex set of a random graph where each possible edge is present with probability pe. We do not know which edges are actually present unless we scan/probe an edge. However whenever we probe an edge and find it to be present, we are constrained to… (More)

Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications in many areas. Recently, there has been significant interest in extending the theory of algorithms for optimizing… (More)

We consider the following stochastic optimization problem first introduced by Chen et al. in [7]. We are given a vertex set of a random graph where each possible edge is present with probability pe. We do not know which edges are actually present unless we scan/probe an edge. However whenever we probe an edge and find it to be present, we are constrained to… (More)

Motivated by economic thought, a recent research agenda has suggested the algo-rithmic study of combinatorial optimization problems under functions which satisfy the property of decreasing marginal cost. A natural first step to model such functions is to consider submod-ular functions. However, many fundamental problems have turned out to be extremely hard… (More)

- Pushkar Tripathi, Ozlem Ergun, Maira Florina Balcan, B. M. Tripathi
- 2012

for inspiring me to follow my dreams. iii ACKNOWLEDGEMENTS I would like to thank my advisor Vijay Vazirani, for his constant support and motivation throughout my graduate studies and for being so patient with me. His wisdom and insight were instrumental in the successful completion of this thesis. I was fortunate to work with Prasad Tetali towards the end… (More)