In this paper we consider single machine SLK due date assignment scheduling problem with a rate-modifying activity. In this model, the machine has a rate-modifying activity that can change the processing rate of machi...
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In this paper we consider single machine SLK due date assignment scheduling problem with a rate-modifying activity. In this model, the machine has a rate-modifying activity that can change the processing rate of machine under consideration. Hence the actual processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. We need to make a decision on when to schedule the rate-modifying activity, the optimal common flow allowance and the sequence of jobs to minimize total earliness, tardiness and common flow allowance cost. We introduce an efficient (polynomial time) solution for this problem. (C) 2010 Elsevier Ltd. All rights reserved.
We consider the flowshop problem with unit-time operations and intree precedence constraints, with the objective to minimize the total completion time. We present a polynomial-time algorithm assuming that the number o...
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We consider the flowshop problem with unit-time operations and intree precedence constraints, with the objective to minimize the total completion time. We present a polynomial-time algorithm assuming that the number of machines is fixed. This proves a recently stated conjecture. (C) 2004 Elsevier B.V. All rights reserved.
A bound is given for the average length of a ‘lexicographic path’, a definition that is motivated by degeneracies encountered when using the randomized simplex method.
A bound is given for the average length of a ‘lexicographic path’, a definition that is motivated by degeneracies encountered when using the randomized simplex method.
A dominating cycle for a graph G = ( V , E ) is a subset C of V which has the following properties: (i) the subgraph of G induced by C has a Hamiltonian cycle, and (ii) every vertex of V is adjacent to some vertex of ...
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A dominating cycle for a graph G = ( V , E ) is a subset C of V which has the following properties: (i) the subgraph of G induced by C has a Hamiltonian cycle, and (ii) every vertex of V is adjacent to some vertex of C . In this paper, we develop an O ( n 2 ) algorithm for finding a minimum cardinality dominating cycle in a permutation graph. We also show that a minimum cardinality dominating cycle in a permutation graph always has an even number of vertices unless it is isomorphic to C 3 .
Suppose that p traveling salesmen must visit together all points of a tree, and the objective is to minimize the maximum of the lengths of their tours. The location-allocation version of the problem (where both optima...
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Suppose that p traveling salesmen must visit together all points of a tree, and the objective is to minimize the maximum of the lengths of their tours. The location-allocation version of the problem (where both optimal home locations of the salesmen and their optimal tours must be found) is known to be NP-hard for any pgreater than or equal to2. We present exact polynomial algorithms with a linear order of complexity for location versions of the problem (where only optimal home locations must be found, without the corresponding tours) for the cases p=2 and p=3.
Let lambda(N) denote the weight of a minimum cut in an edge-weighted undirected network N, and n and m denote the numbers of vertices and edges, respectively. It is known that O(n(2k)) is upper bound on the number of ...
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Let lambda(N) denote the weight of a minimum cut in an edge-weighted undirected network N, and n and m denote the numbers of vertices and edges, respectively. It is known that O(n(2k)) is upper bound on the number of cuts with weights less than k lambda(N), where k greater than or equal to 1 is a given constant. This paper first shows that all cuts of weights less than k lambda(N) can be enumerated in O(m(2)n + n(2k)m) time without using the maximum flow algorithm. The paper then proves for k < 4/3 that ((n)(2)) is a tight upper bound on the number of cuts of weights less than k lambda(N), and that all those cuts can be enumerated in O(m(2)n + mn(2) log n) time.
We propose techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization and nonlinear programming problems. Our techniques find the optimal solution value and the optimal dual...
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We propose techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization and nonlinear programming problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in problems of a certain structure our techniques find not only the optimal solution value, but the solution as well. Our techniques lead to significant improvements in the theoretical running time compared with previously known methods (interior point methods, Ellipsoid algorithm, Vaidya's algorithm). We use our method to the solution of the LP relaxation and the Langrangean dual of several classical combinatorial problems, like the traveling salesman problem, the vehicle routing problem, the Steiner tree problem, the k-connected problem, multicommodity flows, network design problems, network flow problems with side constraints, facility location problems, K-polymatroid intersection, multiple item capacitated lot sizing problem, and stochastic programming. In all these problems our techniques significantly improve the theoretical running time and yield the fastest way to solve them.
Splitting a tree is defined as removing all edges of a chain and disconnecting one from the other edges incident with that chain. Splitting a forest is simultaneously splitting each of its non-trivial trees. The split...
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Splitting a tree is defined as removing all edges of a chain and disconnecting one from the other edges incident with that chain. Splitting a forest is simultaneously splitting each of its non-trivial trees. The splitting number sigma(T) of a tree T is the minimum number of successive forest splittings which lead to deletion of all of T's edges. An O (N) algorithm is proposed to get an upper bound sigma'(t), the connected splitting number, on the splitting number sigma(t) of a tree T and an O(N log N) algorithm to compute this last number, where N is the number of vertices of the tree. Subject to a mild condition, these numbers lead to find a 'black-and-white coloring' of a tree T. In such a coloring a large part of T's vertices are colored in black or white and no two adjacent vertices receive a different color.
In this paper we present a graph-theoretic polynomial algorithm which has positive probability of finding a Hamiltonian path in a given graph, if there is one; if the algorithm fails, it can be rerun with a randomly c...
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In this paper we present a graph-theoretic polynomial algorithm which has positive probability of finding a Hamiltonian path in a given graph, if there is one; if the algorithm fails, it can be rerun with a randomly chosen starting solution, and there is again a positive probability it will find an answer. If there is no Hamiltonian path, the algorithm will always terminate with failure. We call this a Successful algorithm because it has high (close to 1) empirical probability of success and it works in polynomial time. Some basic theoretical results concerning spanning arborescences of a graph are given. The concept of a ramification index is defined and it is shown that ramification index of a Hamiltonian path is zero. The algorithm starts with finding any spanning arborescence and by suitable pivots it endeavors to reduce the ramification index to zero. Probabilistic properties of the algorithm are discussed. Computational experience with graphs up to 30 000 nodes is included.
We give a polynomial time algorithm that finds the maximum weight stable set in a graph that does not contain an induced path on seven vertices or a bull (the graph with vertices a, b, c, d, e and edges ab, bc, cd, be...
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We give a polynomial time algorithm that finds the maximum weight stable set in a graph that does not contain an induced path on seven vertices or a bull (the graph with vertices a, b, c, d, e and edges ab, bc, cd, be, ce). With the same arguments we also give a polynomial algorithm for any graph that does not contain S-1,S-2,S-3 or a bull. (C) 2017 Elsevier B.V. All rights reserved.
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