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We 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. We 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 under(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 min-cut, max-flow problem, and can be solved in polynomial time. We show that the problem(More)
Many combinatorial optimization problems call for the optimization of a linear function over a certain polytope. Typically, these polytopes have an exponential number of facets. We explore the problem of finding small linear programming formulations when one may use any new variables and constraints. We show that expressing the matching and the Traveling(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)
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(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)
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)
We present an algorithm that generates all maximal independent sets of a graph in lexicographic order, with only polynomial delay between the output of two successive independent sets. We also show that there is no polynomial-delay algorithm for generating all maximal independent sets in reverse lexicographic order, unless P = NP. Generating all(More)