Clifford Stein

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problems<lb>To understand the class of polynomial-time solvable problems, we must first have a formal<lb>notion of what a "problem" is. We define an abstract problem Q to be a binary relation on a<lb>set I of problem instances and a set S of problem solutions. For example, an instance for<lb>SHORTEST-PATH is a triple consisting of a graph and two vertices.(More)
We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worst-case analysis, no good on-line algorithms exist for these problems, and for some variants(More)
We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with(More)
This paper present a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph's minimum cut form an extremely small fraction of the graph's edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high(More)
A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time(More)
In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine, and the aim is to complete all jobs as quickly as possible. This problem is strongly AfP-hard even for very restrictive special cases. We give the first randomized and deterministic(More)
including environments with parallelizable jobs, jobs contending for shared resources, tree precedence-constrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved on-line. Finally, one of the consequences of our work is the surprising structural property that there are schedules(More)
We show that for low-density parity-check (LDPC) codes whose Tanner graphs have sufficient expansion, the linear programming (LP) decoder of Feldman, Karger, and Wainwright can correct a constant fraction of errors. A random graph will have sufficient expansion with high probability, and recent work shows that such graphs can be constructed efficiently. A(More)