A problem of batching identical jobs on a single machine is studied. Constant processing times and batch setup times are assumed. An algorithm is presented to minimize the sum over all jobs of the batched completion t...
详细信息
A problem of batching identical jobs on a single machine is studied. Constant processing times and batch setup times are assumed. An algorithm is presented to minimize the sum over all jobs of the batched completion times, and shown to run in time polynomial in the logarithms of the problem parameters.
We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectang...
详细信息
We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectangular pieces. A polynomial time algorithm is described to construct the convex hull of solutions to this problem. (C) 2007 Published by Elsevier B.V.
Submodular flow problems, introduced by Edmonds and Giles [2], generalize network flow problems. Many algorithms for solving network flow problems have been generalized to submodular flow problems (cf. references in F...
详细信息
Submodular flow problems, introduced by Edmonds and Giles [2], generalize network flow problems. Many algorithms for solving network flow problems have been generalized to submodular flow problems (cf. references in Fujishige [4]), e.g. the cycle canceling method of Klein [9]. For network flow problems, the choice of minimum-mean cycles in Goldberg and Tarjan [6], and the choice of minimum-ratio cycles in Wallacher [12] lead to polynomial cycle canceling methods. For submodular flow problems, Cui and Fujishige [1] show finiteness for the minimum-mean cycle method while Zimmermann [16] develops a pseudo-polynomial minimum ratio cycle method. Here, we prove pseudo-polynomiality of a larger class of the minimum-ratio variants and, by combining both methods, we develop a polynomial cycle canceling algorithm for submodular flow problems.
We present a primal simplex algorithm that solves the assignment problem in 1/2n(n+3)-4 pivots. Starting with a problem of size 1, we sequentially solve problems of size 2,3,4,...,n. The algorithm utilizes degeneracy ...
详细信息
We present a primal simplex algorithm that solves the assignment problem in 1/2n(n+3)-4 pivots. Starting with a problem of size 1, we sequentially solve problems of size 2,3,4,...,n. The algorithm utilizes degeneracy by working with strongly feasible trees and employs Dantzig's rule for entering edges for the subproblem. The number of nondegenerate simplex pivots is bounded by n-1. The number of consecutive degenerate simplex pivots is bounded by 1/2(n-2)(n+1). All three bounds are sharp. The algorithm can be implemented to run in O(n3) time for dense graphs. For sparse graphs, using state of the art data structures, it runs in O(n2 log n+nm) time, where the bipartite graph has 2n nodes and m edges.
Data flow machines whose task graphs are acyclic can be transformed into synchronous machines, thereby increasing pipelining and throughput. This is achieved by introducing delays or buffers on certain lines, so that ...
详细信息
Data flow machines whose task graphs are acyclic can be transformed into synchronous machines, thereby increasing pipelining and throughput. This is achieved by introducing delays or buffers on certain lines, so that the resulting graph is balanced, i.e., travel times along any two paths with common endpoints are the same. The buffer assignment problem is how to balance a rooted acyclic data flow graph with a minimum number of buffer units. Recently, an integer programming decomposition procedure was proposed for this problem. The decomposition was introduced in an attempt to circumvent the exponential blowup typical to integer programming algorithms. In this paper, we show that the buffer assignment problem can in fact be solved to optimality in low-degree polynomial time. The result is obtained by a sequence of reformulations of the problem, leading to models to which simple and efficient network flow procedures can be successfully applied.
A polynomial algorithm for the multiple bounded knapsack problem with divisible item sizes is presented. The complexity of the algorithm is O(n(2) + nm), where n and m are the number of different item sizes and knapsa...
详细信息
A polynomial algorithm for the multiple bounded knapsack problem with divisible item sizes is presented. The complexity of the algorithm is O(n(2) + nm), where n and m are the number of different item sizes and knapsacks, respectively. It is also shown that the algorithm complexity reduces to O (n log n + mm) when a single copy exists of each item. (C) 2009 Published by Elsevier B.V.
In this paper we consider the open shop problem with unit processing times and tree constraints among the jobs. The objective is to mimimize the schedule length C(max). The complexity of this problem was open. We pres...
详细信息
In this paper we consider the open shop problem with unit processing times and tree constraints among the jobs. The objective is to mimimize the schedule length C(max). The complexity of this problem was open. We present a polynomial algorithm which decomposes the problem into subproblems by means of the occurrence of unavoidable idle times. We consider two types of subproblems which can be solved by constructing special latin rectangles.
This paper presents polynomially bounded algorithms for finding a cycle through any two prescribed arcs in a semicomplete digraph and for finding a cycle through any two prescribed vertices in a complete k-partite ori...
详细信息
This paper presents polynomially bounded algorithms for finding a cycle through any two prescribed arcs in a semicomplete digraph and for finding a cycle through any two prescribed vertices in a complete k-partite oriented graph. It is also shown that the problem of finding a maximum transitive subtournament of a tournament and the problem of finding a cycle through a prescribed arc set in a tournanment are both NP-complete.
In this paper the classical stable roommates problem is generalized to situations when the two partners in a pair perform different roles. We propose an efficient algorithm to decide the existence of a stable matching...
详细信息
In this paper the classical stable roommates problem is generalized to situations when the two partners in a pair perform different roles. We propose an efficient algorithm to decide the existence of a stable matching in this problem. (C) 2003 Elsevier B.V. All rights reserved.
This paper introduces the continuous minimax knapsack problem with generalized lower bound constraints and describes an algorithm that solves this problem in O(n logn) time. We also discuss the related problem with ge...
详细信息
This paper introduces the continuous minimax knapsack problem with generalized lower bound constraints and describes an algorithm that solves this problem in O(n logn) time. We also discuss the related problem with generalized upper bound constraints.
暂无评论