Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x ≥ 0,y ≥ 0,x i y i = 0 (i = 1, 2,?,n) is known as a linear complementarity problem...
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Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x ≥ 0,y ≥ 0,x i y i = 0 (i = 1, 2,?,n) is known as a linear complementarity problem. Under the assumption thatM is positive semidefinite, this paper presents an algorithm that solves the problem in O(n 3 L) arithmetic operations by tracing the path of centers,{(x, y) ∈ S: x i y i =μ (i = 1, 2,?,n) for some μ > 0} of the feasible regionS = {(x, y) ≥ 0:y = Mx + q}, whereL denotes the size of the input data of the problem.
The complexity of group testing is a long-standing open problem. Recently, Du and Ko studied some related problems which can explain the hardness of group testing undirectly. One of such problems is called the determi...
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The complexity of group testing is a long-standing open problem. Recently, Du and Ko studied some related problems which can explain the hardness of group testing undirectly. One of such problems is called the determinacy problem on which they left open questions for some models. In this paper, we answer all of them.
Define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis. An algorithm is given that finds a cycle basis with the shortest possible length in O(m3n<span cla...
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Define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis. An algorithm is given that finds a cycle basis with the shortest possible length in O(m3n
Seymour has introduced a class of matrices for which the polyhedron { x | Ax ≥ 1, x ≥ 0} has all integral extreme points. T main result of this paper is a polynomial-time algorithm for determining whether a given ma...
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Seymour has introduced a class of matrices for which the polyhedron { x | Ax ≥ 1, x ≥ 0} has all integral extreme points. T main result of this paper is a polynomial-time algorithm for determining whether a given matrix is in this class.
polynomial-time algorithms are presented for solving combinatorial packing and covering problems defined from the integral feasible flows in an integral supply-demand network. These algorithms are also shown to apply ...
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polynomial-time algorithms are presented for solving combinatorial packing and covering problems defined from the integral feasible flows in an integral supply-demand network. These algorithms are also shown to apply to packing and covering problems defined by the minimal integral solutions to general totally unimodular systems. Analogous problems arising from matroid bases are also discussed and it is demonstrated that a means for solving such problems is provided by recent work of Cunningham.
The problem of determining a minimum total dominating set along with several closely related problems has been investigated remarkably. For general graphs, the total dominating set problem is computationally intracta...
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The problem of determining a minimum total dominating set along with several closely related problems has been investigated remarkably. For general graphs, the total dominating set problem is computationally intractable. Actually, it is an NP-complete problem. Thus, it is very unlikely that this problem can be solved by an efficient algorithm whose running time is bounded by a polynomial in the size of the input. The total dominating set problem also is NP-complete for special classes of graphs, such as bipartite graphs, split graphs, and undirected path graphs. Interval graphs represent intersecting intervals on the line. An O(n-squared) timealgorithm for finding a minimum total dominating set in an interval graph by reducing it to a shortest path problem on an appropriate acyclic directed network is presented. The type of reduction used can easily be modified to work in the weighted case also.
In this correspondence, we study the problem of finding optimal reconfiguration strategies for a class of reconfigurable fault- tolerant computer systems in which there is no repair in failed components. The problem o...
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In this correspondence, we study the problem of finding optimal reconfiguration strategies for a class of reconfigurable fault- tolerant computer systems in which there is no repair in failed components. The problem of finding optimal reconfiguration strategies consists of determining, for each failed state of the system, the operational state into which the system should reconfigure itself. We presented a stochastic model for the above class of reconfigurable computer systems. Based on this model, we construct a polynomial-time algorithm for finding optimal reconfiguration strategies.
The complexity of linear programming is discussed in the "integer" and "real number" models of computation. Even though the integer model is widely used in theoretical computer science, the real nu...
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The following class of matching problems is considered. The vertices of a complete undirected graph are indexed 1,⋯,n1,⋯,n1, \cdots,n, where <span class="MathJax" id="MathJax-Element-5-Frame" ta...
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