A new model of task system in which the execution time of a task depends on its starting time is considered. It is shown that the feasibility problem on a single processor is NP-complete for a set of tasks with identi...
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A new model of task system in which the execution time of a task depends on its starting time is considered. It is shown that the feasibility problem on a single processor is NP-complete for a set of tasks with identical release times and two distinct deadlines. An O(n log n)-timealgorithm is given for a set of tasks with identical release times and deadlines. These two results give a sharp boundary delineating the complexity of the problem.
Recently several new results have been developed for the asymptotic (local) convergence of polynomial-time interior-point algorithms. It has been shown that the predictor-corrector algorithm for linear programming (LP...
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Recently several new results have been developed for the asymptotic (local) convergence of polynomial-time interior-point algorithms. It has been shown that the predictor-corrector algorithm for linear programming (LP) exhibits asymptotic quadratic convergence of the primal-dual gap to zero, without any assumptions concerning nondegeneracy, or the convergence of the iteration sequence. In this paper we prove a similar result for the monotone linear complementarity problem (LCP), assuming only that a strictly complementary solution exists. We also show by example that the existence of a strictly complementarity solution appears to be necessary to achieve superlinear convergence for the algorithm.
A procedure is given for recognizing sets of inference rules that generate polynomialtime decidable inference relations. The procedure can automatically recognize the tractability of the inference rules underlying co...
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A procedure is given for recognizing sets of inference rules that generate polynomialtime decidable inference relations. The procedure can automatically recognize the tractability of the inference rules underlying congruence closure. The recognition of tractability for that particular rule set constitutes mechanical verification of a theorem originally proved independently by Kozen and Shostak. The procedure is algorithmic, rather than heuristic, and the class of automatically recognizable tractable rule sets can be precisely characterized. A series of examples of rule sets whose tractability is nontrivial, yet machine recognizable, is also given. The technical framework developed here is viewed as a first step toward a general theory of tractable inference relations.
A k-extremal point set is a point set on the boundary of a k-sided rectilinear convex hull. Given a k-extremal point set of size n, we present an algorithm that computes a rectilinear Steiner minimal tree in time O(k4...
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A k-extremal point set is a point set on the boundary of a k-sided rectilinear convex hull. Given a k-extremal point set of size n, we present an algorithm that computes a rectilinear Steiner minimal tree in time O(k4n). For constant k, this algorithm runs in O(n) time and is asymptotically optimal and, for arbitrary k, the algorithm is the fastest known for this problem,
We consider the complexity of restricted colorings of a graph in which each vertex (or edge) receives one color from a list of permissible colors associated with that vertex (edge). Since the problem is strongly NP-co...
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We consider the complexity of restricted colorings of a graph in which each vertex (or edge) receives one color from a list of permissible colors associated with that vertex (edge). Since the problem is strongly NP-complete, we assume various restrictions imposed on the number and form of permissible colors and the structure of a graph. In this way we obtain some evidence for comparing the complexity of the restricted vertex coloring problem versus that of edge coloring and arrive at a number of results about special cases that are either positive (polynomial solvability) or negative (NP-completeness proofs).
We present a path-following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour. This is done both for the problem in standard form and for its dual pr...
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We present a path-following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour. This is done both for the problem in standard form and for its dual problem. We also discuss some implementation strategies.
A polynomial-time algorithm for a class of linear complementarity problems with positive semidefinite matrices is presented. The method is based on a one-step Euler's prediction and one-step Newton's correctio...
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A polynomial-time algorithm for a class of linear complementarity problems with positive semidefinite matrices is presented. The method is based on a one-step Euler's prediction and one-step Newton's correction procedure to follow the homotopy path defined as the set {(x, y) epsilon R-+(n): x(i)Y(i)=mu, i = 1,.., n, mu > 0, y = Mx + q}, and solves the problem in O(n(3.5)L) arithmetic operations. Moreover, after one iteration the value x(T)y decreases with the ratio at least (1-(2/5 root n)).
The problem of counting the number of cuts with the minimum cardinality in an undirected multigraph arises in various applications such as testing the super-lambda-ness of a graph and calculating upper and lower bound...
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The problem of counting the number of cuts with the minimum cardinality in an undirected multigraph arises in various applications such as testing the super-lambda-ness of a graph and calculating upper and lower bounds on the probabilistic connectedness of a stochastic graph G in which edges are subject to failure. This paper shows that the number \C(G)\ of cuts with the minimum cardinality lambda(G) in a multiple graph G = (V, E) can be computed in O(\E\ + lambda(G)\V\2 + lambda(G)\C(G) parallel-to V\) time.
A few years ago a researcher attempted to show that one could minimize the total schedule length of lots of unit-time jobs by level scheduling. Unfortunately, this method can fail on problems where jobs have successor...
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A few years ago a researcher attempted to show that one could minimize the total schedule length of lots of unit-time jobs by level scheduling. Unfortunately, this method can fail on problems where jobs have successors at more than one level. In this paper, the method is altered to handle this problem.
We obtain a polynomial-time algorithm to compute the supremum of the max-min powers of a map from the Cartesian product of a set to a bounded subset of the real numbers. It is also shown that the value at a pair (x, y...
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We obtain a polynomial-time algorithm to compute the supremum of the max-min powers of a map from the Cartesian product of a set to a bounded subset of the real numbers. It is also shown that the value at a pair (x, y) is equal to the maximum of the first k powers of the map where k is the diameter between x and y in a graph corresponding to the map. A characterization is obtained of the metric introduced by Rosenfeld (1975) for a fuzzy graph.
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