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- Leslie G. Valiant, Vijay V. Vazirani
- STOC
- 1985

For all known NP-complete problems the number of solutions in instances having solutions may vary over an exponentially large range. Furthermore, most of the well-known ones, such as satisfiability, are parsimoniously interreducible, and these can have any number of solutions between zero and an exponentially large number. It is natural to ask whether the… (More)

- Naveen Garg, Vijay V. Vazirani, Mihalis Yannakakis
- SIAM J. Comput.
- 1993

Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: min multicut O(log k) ~ max flow ~ min multicut, where k is the number of commodities. Our proof is constructive; it enables us to find a multicut within O(log k) of the max flow (and… (More)

- Kamal Jain, Vijay V. Vazirani
- J. ACM
- 2001

We present approximation algorithms for the metric uncapacitated facility location problem and the metric <italic>k</italic>-median problem achieving guarantees of 3 and 6 respectively. The distinguishing feature of our algorithms is their low running time: <italic>O(m</italic> log<italic>m</italic>) and <italic>O(m</italic> log<italic>m(L</italic> + log… (More)

- Kamal Jain, Mohammad Mahdian, Evangelos Markakis, Amin Saberi, Vijay V. Vazirani
- J. ACM
- 2003

In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP. This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem. Their approximation factors are 1.861 and 1.61, with running times of <i>O</i>(<i>m</i> log <i>m</i>) and… (More)

- Silvio Micali, Vijay V. Vazirani
- 21st Annual Symposium on Foundations of Computer…
- 1980

In this paper we present an 0(√|V|¿|E|) algorithm for finding a maximum matching in general graphs. This algorithm works in 'phases'. In each phase a maximal set of disjoint minimum length augmenting paths is found, and the existing matching is increased along these paths. Our contribution consists in devising a special way of handling blossoms,… (More)

- Ketan Mulmuley, Umesh V. Vazirani, Vijay V. Vazirani
- Combinatorica
- 1987

A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computa-tionally non-trivial step required in its execution is the inversion of a single integer matrix. Since this step can be parallelized, we get a simple parallel (RNC2) algorithm. At the heart of our algorithm lies a proba-bilistic… (More)

The class of problems involving the random generation of combinatorial structures from a uniform distribution is considered. Uniform generation problems are, in computational difficulty, intermediate between classical existence and counting problems. It is shown that exactly uniform generation of 'efficiently verifiable' combinatorial structures is… (More)

- Naveen Garg, Vijay V. Vazirani, Mihalis Yannakakis
- Algorithmica
- 1997

We study the maximum integral multicommodity flow problem and the minimum multicut problem restricted to trees. This restriction is quite rich and contains as special cases classical optimization problems such as matching and vertex cover for general graphs. It is shown that both the maximum integral multicommodity flow and the minimum multicut problem are… (More)