Mihalis Yannakakis

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W e define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are classes of optimization problems, and in fact contain several natural, well-studied ones. W e show that problems in these classes can be approximated with some bounded error. Furthermore, we show that a number of common optimization problems are complete for MAXSNP(More)
We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifically, there is an E > 0 such that Graph Coloring cannot be approximated with ratio n’ unless P = NP. Set Covering cannot be approximated with ratio c log n for any c < l/4 unless(More)
With advanced computer technology, systems are getting larger to fulfill more complicated tasks, however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This motivates the study of testing finite state machines to ensure(More)
In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. We show that the problem(More)
We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that(More)
Chordal graphs arise naturally in the study of Gaussian elimination on sparse symmetric matrices; acyclic hypergraphs arise in the study of relational data bases. Rose, Tarjan and Lueker [SIAM J. Comput., 5 (1976), pp. 266-283] have given a linear-time algorithm to test whether a graph is chordal, which Yannakakis has modified to test whether a hypergraph(More)
A class of database schemes, called acychc, was recently introduced. It is shown that this class has a number of desirable properties. In particular, several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity. In addition, several equivalent charactenzauons of the class m terms(More)
Generating all configurations that satisfy a given specification (e.g., all permutations of n objects that do not fix any object) is a well-studied problem in combinatorics [6]. Graph theory suggests many interesting problems of this type (see, e.g., [7]). Among them, generating all maximal independent sets of a given graph is one that has attracted(More)
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)
Scenario based speci cations such as message sequence charts MSC o er an intuitive and visual way of describing design require ments Such speci cations focus on message exchanges among communi cating entities in distributed software systems Structured speci cations such as MSC graphs and Hierarchical MSC graphs HMSC allow con venient expression of multiple(More)