In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n epsilon-...
详细信息
In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n epsilon-separated segments in two dimensional space. Our results are based on an interesting combinatorial result which bounds the total number of entry points in an optimal TSP tour and a generalization of Arora's technique(5) for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n(2)(log n)(O(1/e2))) time to compute a (1 + epsilon)-approximation with probability greater than or equal to 1/2, and can be derandomized with an additional factor of O(n(2)).
Given a set S = {s(1), s(2), ..., s(n)} of strings each of length m, and an integer L, we study the following two problems. k-CLOSEST SUBSTRING problem: find k center strings c(1), c(2), ..., c(k) of length L minimizi...
详细信息
ISBN:
(纸本)354022341X
Given a set S = {s(1), s(2), ..., s(n)} of strings each of length m, and an integer L, we study the following two problems. k-CLOSEST SUBSTRING problem: find k center strings c(1), c(2), ..., c(k) of length L minimizing d such that for each s(j) is an element of S, there is a length-L substring t(j) (closest substring) of s(j) with min(1less than or equal toiless than or equal tok) d(c(i), t(j)) less than or equal to d. We give a PTAS for this problem, for k = O(1). k-CONSENSUS PATTERN problem: find k median strings c(1), c(2), ..., c(k) of length L and a substring tj (consensus pattern) of length L from each s(j) minimizing the total cost w = Sigma(j=1)(n) min(1less than or equal toiless than or equal tok) d(c(i), t(j)). We give a PTAS for this problem, for k = O(1). Our results improve recent results of [10] and [16] both of which depended on the random linear transformation technique in [16]. As for general k case, we give an alternative and direct proof of the NP-hardness of (2-epsilon)-approximation of the HAMMING RADIUS k-CLUSTERING problem, a special case of the k-CLOSEST SUBSTRING problem restricted to L = m.
In this paper we investigate the two-stage multiprocessor flow shop scheduling problem F2(P)\ . \C-max, where the numbers m(1) and m(2) of machines available in the two stages are part of the input. We demonstrate the...
详细信息
In this paper we investigate the two-stage multiprocessor flow shop scheduling problem F2(P)\ . \C-max, where the numbers m(1) and m(2) of machines available in the two stages are part of the input. We demonstrate the existence of a polynomial time approximation scheme for this problem. This result solves the simplest case of an open problem that has been posed by Leslie Hall in a recent paper (Hall, 1995). hn extension of our algorithm yields an approximationscheme for the closely related two-stage multiprocessor job shop problem. (C) 2000 Elsevier Science B.V. All rights reserved.
In the module allocation problem we are given n tasks t(1),...,t(n) to be executed by m processors P-1,...,P-m, subject to both execution and communication costs. The cost of any assignment of the tasks to the process...
详细信息
In the module allocation problem we are given n tasks t(1),...,t(n) to be executed by m processors P-1,...,P-m, subject to both execution and communication costs. The cost of any assignment of the tasks to the processors is defined as the sum of the corresponding execution costs, and the communication costs for any pair of tasks assigned to distinct processors. We consider the case where all the tasks communicate with communication costs all equal to a constant c(0). When the number of processors is bounded, we give two exact, polynomial-time algorithms, an elementary one for the case where the execution costs take only two distinct values and one for the general case. When the number of processors is not bounded, we obtain a polynomial-timeapproximationscheme. We obtain a similar algorithm when the communication graph is the edge union of a bounded number of cliques and complete bipartite graphs. (C) 2003 Published by Elsevier B.V.
A t-spanner of an undirected, unweighted graph G is a spanning subgraph S of G with the added property that for every pair of vertices in G, the distance between them in S is at most t times the distance between them ...
详细信息
We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machi...
详细信息
ISBN:
(纸本)3540422870
We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine is specified by an arbitrary vector) at the other end. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms are known for even the most general machine environment of unrelated machines. Recently a PTAS was discovered for the case of identical parallel machines [1]. In contrast, the problem is MAX SNP-hard for unrelated machines [11]. An important open problem was to determine the approximability of the intermediate case of uniformly related machines where each machine has a speed and it takes p/s time to process a job of size p on a machine with speed s. We resolve the complexity of this problem by obtaining a PTAS. This improves the earlier known approximation ratio of (2 + epsilon).
暂无评论