We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this s...
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We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this set are constant, while other ones are either proportional or linear functions of the job starting times. The applied criteria of schedule optimality include the maximum completion time, the total completion time, the total weighted completion time, the maximum lateness and the number of tardy jobs. We delineate a sharp boundary between computationally easy and difficult problems, showing polynomially solvable and NP-hard cases. (C) 2010 Elsevier Inc. All rights reserved.
The paper introduces the two-machine super-shop scheduling problem to minimize makespan. The well-known flow-shop, open-shop, job-shop and mixed-shop scheduling problems are special cases of our model. A polynomial-ti...
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The paper introduces the two-machine super-shop scheduling problem to minimize makespan. The well-known flow-shop, open-shop, job-shop and mixed-shop scheduling problems are special cases of our model. A polynomial-time algorithm to find both pre-emptive and non-pre-emptive optimal schedules is described.
We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases...
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We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomialtime, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomialtime.
Given 2 disjoint graphs and a vertex w in the first graph, the graph G obtained by first removing w from the first graph and then making every vertex in the 2nd graph adjacent to all the neighbors of w in the first gr...
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Given 2 disjoint graphs and a vertex w in the first graph, the graph G obtained by first removing w from the first graph and then making every vertex in the 2nd graph adjacent to all the neighbors of w in the first graph is said to arise by substitution from the first graph to the 2nd. The theoretical importance of substitution was highlighted by Lovasz (1972). His fundamental result asserting that a graph is perfect if and only if its complement is perfect relies on the fact that substitution preserves perfection. Moreover, detecting whether a graph G is substitution-composite can be done in polynomialtime. A characterization of forbidden configurations of the closure of triangle-free graphs (strictly containing the bipartite graphs) under substitution is presented.
This paper addresses the problem of finding the route with maximum end-to-end spectral efficiency, under the constraint of equal bandwidth sharing, in multihop wireless networks. This problem has been addressed recent...
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This paper addresses the problem of finding the route with maximum end-to-end spectral efficiency, under the constraint of equal bandwidth sharing, in multihop wireless networks. This problem has been addressed recently in the literature, and only exhaustive search with exponential computational complexity or suboptimal heuristics are known. This paper closes the algorithmic gap by introducing two algorithms that provide provably optimal solutions to the problem in polynomial-time. The proposed algorithms rely on the iterative use of a shortest path procedure. Our computational results further illustrate the efficiency of the proposed approach.
A spherical code is a finite set X of points lying on the unit sphere of R(n). For such a set, we define rho(X) as the minimum of the squared distances parallel-tox - yparallel-to2, when x, y is-an-element-of X and x ...
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A spherical code is a finite set X of points lying on the unit sphere of R(n). For such a set, we define rho(X) as the minimum of the squared distances parallel-tox - yparallel-to2, when x, y is-an-element-of X and x not-equal y. Define [GRAPHICS] Chabauty in 1953 and Shannon in 1959 have given a lower bound for R(rho), namely, R(rho) > R(CS)(rho) = 1 - 1/2 log2 rho(4 - rho). The complexity of construction of the spherical codes used in order to get this bound is doubly exponential. The polynomially constructible spherical bound R(pol)(rho) is defined as above with the additional restriction that only families of codes with polynomial complexity of construction are considered. We prove R(pol)(rho) greater-than-or-equal-to R(CS)(rho)/2, if rho less-than-or-equal-to 1.535 .... Denote by tau(X)(n) the number of spheres of equal radius that touch one sphere in the n-dimensional space given by some explicit family X, that is, a family of arrangements of spheres}. The asymptotic polynomially constructible kissing number is theta(pol) = lim sup (log2 tau(X)(n))/n, when X ranges over all polynomially constructible families. We prove theta(pol) greater-than-or-equal-to 2/15 = 0.133 ....
In this paper we show that the following problem, the even simple path (ESP) problem for directed planar graphs, is solvable in polynomialtime: Given: a directed planar graph G = (V, E) and two nodes s (startingnode)...
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In this paper we show that the following problem, the even simple path (ESP) problem for directed planar graphs, is solvable in polynomialtime: Given: a directed planar graph G = (V, E) and two nodes s (startingnode);t (targetnode) is an element of V;Find: a simple path (i.e., without repeated nodes) from s to t of even length. (The length of the path is the number of edges it contains.).
This paper provides a polynomial-time algorithm to estimate returns to scale in FDH models, having many strong computational advantages. The equivalence of this method and the only current approach is proved. (c) 2005...
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This paper provides a polynomial-time algorithm to estimate returns to scale in FDH models, having many strong computational advantages. The equivalence of this method and the only current approach is proved. (c) 2005 Published by Elsevier Ltd.
This paper deals with due date assignment and just-in-time scheduling for single machine and parallel machine problems with equal-size jobs where the objective is to minimize the total weighted earliness-tardiness and...
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This paper deals with due date assignment and just-in-time scheduling for single machine and parallel machine problems with equal-size jobs where the objective is to minimize the total weighted earliness-tardiness and due date cost. These two problems, but with a common due date to be calculated, were shown to be polynomially solvable in O(n(4)) time. We first show that this complexity can be reduced to O(n(3)) by modeling the single machine scheduling problem as an assignment problem without necessary due date enumeration. We next prove that the general case with identical parallel machines and a given set of assignable due dates where the cardinality of this set is bounded by a constant number is still polynomially solvable. (C) 2010 Elsevier B.V. All rights reserved.
This paper presents a polynomial-time algorithm for equivalence under certain semiring congruences. These congruences arise when studying the isomorphism of state spaces for a class of hybrid systems. The area of hybr...
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This paper presents a polynomial-time algorithm for equivalence under certain semiring congruences. These congruences arise when studying the isomorphism of state spaces for a class of hybrid systems. The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides one systematic approach to discrete-time hybrid systems, naturally blending switching mechanisms with classical linear components. PL systems model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism. PL systems are of interest as controllers as well as identification models. Basic questions for any class of systems are those of equivalence, and, in particular, whether state spaces are equivalent under a change of variables. This paper studies this state-space equivalence problem for PL systems. The problem was known to be decidable, but its computational complexity was potentially exponential;here it is shown to be solvable in polynomialtime. (C) 2001 Elsevier Science B.V. All rights reserved.
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