Michael A. Langston

Nonconstructive tools for proving polynomial-time decidability

Recent advances in graph theory and graph algorithms dramatically alter the traditional view of concrete complexity theory, in which a decision problem is generally shown to be in P by producing an efficient algorithm to solve an optimization version of the problem. Nonconstructive tools are now available for classifying problems as decidable in polynomial time by guaranteeing only the existence of polynomial-time decision algorithms. In this paper these new methods are employed to prove membership in P for a number of problems whose complexities are not otherwise known. Powerful consequences of these techniques are pointed out and their utility is illustrated. A type of partially ordered set that supports this general approach is defined and explored.

Variable sized bin packing

In the classical bin packing problem one seeks to pack a list of pieces in the minimum space using unit capacity bins. This paper addresses the more general problem in which a fixed collection of bin sizes is allowed. Three efficient approximation algorithms are described and analyzed. They guarantee asymptotic worst-case performance bounds of 2,

Nonconstructive advances in polynomial-time complexity

{3 / 2}

SCHEDULING TO MAXIMIZE THE MINIMUM PROCESSOR FINISH TIME IN A MULTIPROCESSOR SYSTEM

and

Interstage Transportation Planning in the Deterministic Flow-Shop Environment

{4 / 3}

Practical in-place merging

.

On search decision and the efficiency of polynomial-time algorithms

Abstract The field of computational complexity for concrete, practical combinatorial problems has developed in a remarkably smooth fashion. One can point to several features of the theory of polynomial-time computability which make it especially well-behaved, including: (1) the modelling of feasible computing by polynomial-time complexity is well-supported by the fact that almost all known polynomial-time algorithms for natural problems have running times bounded by polynomials of small degree; (2) problems are invariably known to be decidable in polynomial time by direct evidence in the form of efficient algorithms; (3) while the theory is formulated in terms of decision problems, almost all known algorithms proceed by actually constructing a solution to the problem at hand. Herein we illustrate how recent advances in graph theory and graph algorithms dramatically alter this situation on all three counts. Powerful and easy-to-apply tools are now available for classifying problems as decidable in polynomial time by nonconstructively proving only the existence of polynomial-time decision algorithms. These tools neither specify the degree of the polynomial, nor produce the decision algorithm, nor guarantee that such an algorithm is of any use in constructing a solution. These developments present both practitioners and theories with novel challenges.

Bounds for multifit scheduling on uniform processors

This investigation considers the problem of nonpreemptively assigning a set of independent tasks to a system of identical processors to maximize the earliest processor finishing time. While this goal is a nonstandard scheduling criterion, it does have natural applications in certain maintenance scheduling and deterministic fleet sizing problems. The problem is NP-hard, justifying an analysis of heuristics such as the well-known LPT algorithm in an effort to guarantee near-optimal results. It is proved that the worst-case performance of the LPT algorithm has an asymptotically tight bound of

Evaluation of a MULTIFIT-based scheduling algorithm

frac{4}{3}

Analysis of a compound bin packing algorithm

times the optimal.