We consider the problem faced by a company that wants to use viral marketing to introduce a new product into a market where a competing product is already being introduced. We assume that consumers… (More)

We introduce new problems of finding minimum-cost rankings and clusterings which must be consistent with certain constraints (e.g. an input partial order in the case of ranking problems); we give… (More)

We consider ranking and clustering problems related to the aggregation of inconsistent information. Ailon, Charikar, and Newman [1] proposed randomized constant factor approximation algorithms for… (More)

We consider the problem of finding a ranking of a set of elements that is “closest to” a given set of input rankings of the elements; more precisely, we want to find a permutation that minimizes the… (More)

Determining the precise integrality gap for the subtour LP relaxation of the traveling salesman problem is a significant open question, with little progress made in thirty years in the general case… (More)

For several NP-hard network design problems, the best known approximation algorithms are remarkably simple randomized algorithms called Sample-Augment algorithms in Gupta et al. (J. ACM 54(3):11,… (More)

We present a very simple way of derandomizing the algorithm proposed by Gupta, Kumar and Roughgarden for Single Source Rent-or-Buy by using the method of conditional expectation. Using the improved… (More)

We give deterministic versions of randomized approximation algorithms for several ranking and clustering problems that were proposed by Ailon, Charikar and Newman[1]. We show that under a reasonable… (More)

In this paper, we study the integrality gap of the subtour LP relaxation for the traveling salesman problem in the special case when all edge costs are either 1 or 2. For the general case of… (More)

We consider the feedback vertex set and feedback arc set problems in bipartite tournaments. We improve on recent results by giving a 2-approximation algorithm for the feedback vertex set problem. We… (More)