One of the main issues in flow control problems is deadlock of messages caused by a limited amount of resources. In this paper, the problem of predicting whether a deadlock will necessarily occur in a Store-and-Forwar...
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One of the main issues in flow control problems is deadlock of messages caused by a limited amount of resources. In this paper, the problem of predicting whether a deadlock will necessarily occur in a Store-and-Forward Network is analyzed. We show that, in the case of dynamic routing, the deadlock prediction problem can be decided in polynomial time if tokens are allowed to transit more than once through the same vertex, in contrast with an NP-completeness result in the case where they are allowed to transit at most once.
The Windy Postman Problem (WPP) is defined as follows: Given an undirected connected graphG = (V, E) and costsc ij andc ji for each edgeij ∈E (wherec ij is the cost of traversing edgeij fromi toj), find a windy...
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The Windy Postman Problem (WPP) is defined as follows: Given an undirected connected graphG = (V, E) and costsc ij andc ji for each edgeij ∈E (wherec ij is the cost of traversing edgeij fromi toj), find a windy postman tour of minimum cost. Here, by a windy postman tour, we mean a closed directed walk which is an orientation of a closed walk inG containing each edge ofE at least once.
We present a sequential dual-simplex algorithm for the linear problem which has the same complexity as the algorithms of Balinski [3,4] and Goldfarb [8]: O( n 2 ) pivots, O( n 2 log n + nm ) time. Our algorithm works ...
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We present a sequential dual-simplex algorithm for the linear problem which has the same complexity as the algorithms of Balinski [3,4] and Goldfarb [8]: O( n 2 ) pivots, O( n 2 log n + nm ) time. Our algorithm works with the (dual) strongly feasible trees and can handle rectangular systems quite naturally.
Given a bidirected graphG and a vectorb of positive integral node-weights, an integer linear program IP is defined on (G, b). IP generalizes the node packing problem on a node-weighted (undirected) graph in the sense ...
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Given a bidirected graphG and a vectorb of positive integral node-weights, an integer linear program IP is defined on (G, b). IP generalizes the node packing problem on a node-weighted (undirected) graph in the sense that it reduces to the latter whenG is undirected. A polynomial time algorithm is given that recognizes whether CP (the linear program obtained by relaxing the integrality constraints of IP) has an integral optimal solution. Also an efficient method for solving the linear programming dual of CP is described.
A clutter L is a collection of m subsets of a ground set E ( L ) = { x 1 ,…, x n } with the property that, for every pair A i , A j ϵ L , A i is neither contained nor contains A j , A transversal of L is a subset of ...
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A clutter L is a collection of m subsets of a ground set E ( L ) = { x 1 ,…, x n } with the property that, for every pair A i , A j ϵ L , A i is neither contained nor contains A j , A transversal of L is a subset of E ( L ) intersecting every member of L . If we associate with each element x j ϵ E ( L ) a weight c j , the problem of finding a transversal having minimum weight is equivalent to the following set-covering problem min {c T x|M L x ⩾ 1 m , x j ϵ {0, 1}, j = 1,…, n} where M L is the matrix whose rows are the incidence vectors of the subsets A i ϵ L and 1 m denotes the vector with m ones. A set-covering problem is regular if there exists an ordering of the variables σ = ( x 1 ,…, x n ) such that, for every feasible solution x with x i = 1, x j = 0, j < i , the vector x + e j − e i is also a feasible solution, where e i is the i th unit vector. The matrix M of a regular set-covering problem is said to be regular. A regular clutter is any clutter whose incidence matrix is regular. In this paper we describe some properties of regular clutters and propose an algorithm which, in O( mn ) steps, generates all the minimal transversals of a regular clutter L and produces the transversal having minimum weight.
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...
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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.
Scheduling problems of a batch processing machine are solved by efficient algorithms. On a batch processing machine, multiple jobs can be processed simultaneously in a batch form. We call the number of jobs in the bat...
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Scheduling problems of a batch processing machine are solved by efficient algorithms. On a batch processing machine, multiple jobs can be processed simultaneously in a batch form. We call the number of jobs in the batch the batch size, which can be any integer between 1 and k , a predetermined integer of the maximum batch size. The process time of a batch is constant and independent of the batch size. Preemption is not allowed. Given n jobs with release times r 1 and due dates d i , i = 1…., n , we give efficient algorithms to find a feasible schedule, if any, which minimizes the final completion time under the assumption such that for r i > r j , d i ⩾ d j . Some industrial applications are discussed.
Scaling is a general technique used in transforming the complexity of a linear program from pseudopolynomiality to fully polynomiality. This is done by applying a pseudopolynomial algorithm to a polynomial number of s...
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A NP-hard problem (P) of mixed-discrete linear programming is considered which consists in the minimization of a linear objective function subject to a special nonconnected subset of an unbounded polymatroid. For this...
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This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear ...
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This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear equalities and inequalities. The central notion is that of a 3-edge cutset, namely, a set of 3 edges that, when removed, disconnects the graph. Conversely, our approach can be used to construct classes of graphs for which there exists a polynomial algorithm for the traveling salesman problem. The approach is illustrated on two examples, Halin graphs and prismatic graphs.
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