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We consider the following simple algorithm for feedback arc set problem in weighted tournaments --- order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of 5 if the weights satisfy <i>probability constraints</i> (for any pair of vertices <i>u</i> and <i>v, w</i><inf><i>uv</i></inf> +(More)
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every 0 < R < 1 and ε > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1−R−ε) of worst-case errors. At(More)
Consider a random graph model where each possible edge e is present independently with some probability p e . Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced(More)
A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-disjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the(More)
Motivated by applications in online dating and kidney exchange , we study a stochastic matching problem in which we have a random graph G given by a node set V and probabilities p(i, j) on all pairs i, j ∈ V representing the probability that edge (i, j) exists. Additionally, each node has an integer weight t(i) called its patience parameter. Nodes represent(More)
Motivated by the capabilities of modern storage architectures, we consider the following generalization of the data stream model where the algorithm has sequential access to multiple streams. Unlike the data stream model, where the stream is read only, in this new model (introduced in [8,9]) the algorithms can also write onto streams. There is no limit on(More)
We study the following problem related to pricing over time. Assume there is a collection of bidders, each of whom is interested in buying a copy of an item of which there is an unlimited supply. Every bidder is associated with a time interval over which the bidder will consider buying a copy of the item, and a maximum value the bidder is willing to pay for(More)