This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refuel...
详细信息
This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refueling station to maximize the traffic flow covered in round trips/day. Two reduction properties regarding the problem size and some optimality conditions are derived. Based on these conditions, an exact polynomial algorithm is developed to determine the set of optimal locations for the refueling station. A small tree network example is solved to illustrate the algorithm. (C) 2014 Elsevier Ltd. All rights reserved.
In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and...
详细信息
In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and production planning problems. We discuss fundamental properties associated with the proposed algorithm and analyze the convergence and complexity of the algorithm. (c) 2004 Elsevier Inc. All rights reserved.
In the paper we consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s(1),s(2), and s(3) to minimize the ***. We assume that jobs are subjected to some kind of mutual exclusion constra...
详细信息
In the paper we consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s(1),s(2), and s(3) to minimize the ***. We assume that jobs are subjected to some kind of mutual exclusion constraints, modeled by a cubic incompatibility graph. We show that if the graph is 2-chromatic then. the problem can be solved in 0(n(2)) time. If the graph is 3-chromatic, the problem becomes NP-hard even if s1 > s(2) = s(3). However, in this case there exists a 10/7-approximation algorithm running in 0(n(3)) time. Moreover, this algorithm solves the problem almost surely to optimality if 3(s1)/4 <= s(2) = s(3). (C) 2016 Elsevier B.V. All rights reserved.
This paper is concerned with algorithms and applications of decreasing minimization on an M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on a recent characterization of decre...
详细信息
This paper is concerned with algorithms and applications of decreasing minimization on an M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on a recent characterization of decreasingly minimal (dec-min) elements, we develop a strongly polynomial algorithm for computing a dec-min element of an M-convex set. The matroidal feature of the set of dec-min elements makes it possible to compute a minimum cost dec-min element, as well. Our second goal is to exhibit various applications in matroid and network optimization, resource allocation, and (hyper)graph orientation. We extend earlier results on semi-matchings to a large degree by developing a structural description of dec-min in-degree bounded orientations of a graph. This characterization gives rise to a strongly polynomial algorithm for finding a minimum edge-cost dec-min orientation.
The polynomial algorithms of determining Bayesian network structure are described as "tree" or "polytree". In the known Bayesian network structure consideration is given to Bayesian recognition pro...
详细信息
The polynomial algorithms of determining Bayesian network structure are described as "tree" or "polytree". In the known Bayesian network structure consideration is given to Bayesian recognition procedures built on learning samples by estimations of transition probabilities.
We consider the two problems of finding the maximum number of node disjoint triangles and edge disjoint triangles in an undirected graph. We show that the first (respectively second) problem is polynomially solvable i...
详细信息
We consider the two problems of finding the maximum number of node disjoint triangles and edge disjoint triangles in an undirected graph. We show that the first (respectively second) problem is polynomially solvable if the maximum degree of the input graph is at most 3 (respectively 4), whereas it is APX-hard for general graphs and NP-hard for planar graphs if the maximum degree is 4 (respectively 5) or more. (C) 2002 Elsevier Science B.V. All rights reserved.
Gutjahr, Welzl and Woeginger found polynomial-time algorithms for a number of digraph homomorphism problems. These algorithms are based on the (X) under bar -enumeration, the C-k-extended (X) under bar -enumeration an...
详细信息
Gutjahr, Welzl and Woeginger found polynomial-time algorithms for a number of digraph homomorphism problems. These algorithms are based on the (X) under bar -enumeration, the C-k-extended (X) under bar -enumeration and the (X) under bar -graft construction. In this note, we show how the last two methods can be combined to obtain new polynomial-time algorithms, which also work for list homomorphisms. In the process, we are able to extend results of Bang-Jensen and Hell, dealing with homomorphisms to bipartite tournaments, to list homomorphisms. (C) 2011 Elsevier B.V. All rights reserved.
We study vertex colourings of digraphs so that no out-neighbourhood is monochromatic and call such a colouring an out-colouring. The problem of deciding whether a given digraph has an out-colouring with only two colou...
详细信息
We study vertex colourings of digraphs so that no out-neighbourhood is monochromatic and call such a colouring an out-colouring. The problem of deciding whether a given digraph has an out-colouring with only two colours (called a 2-out-colouring) is NP-complete. We show that for every choice of positive integers r,k there exists a k-strong bipartite tournament, which needs at least r colours in every out-colouring. Our main results are on tournaments and semicomplete digraphs. We prove that, except for the Paley tournament P7, every strong semicomplete digraph of minimum out-degree at least three has a 2-out-colouring. Furthermore, we show that every semicomplete digraph on at least seven vertices has a 2-out-colouring if and only if it has a balanced such colouring, that is, the difference between the number of vertices that receive colour 1 and colour 2 is at most one. In the second half of the paper, we consider the generalization of 2-out-colourings to vertex partitions (V1,V2) of a digraph D so that each of the three digraphs induced by respectively, the vertices of V1, the vertices of V2 and all arcs between V1 and V2, have minimum out-degree k for a prescribed integer k >= 1. Using probabilistic arguments, we prove that there exists an absolute positive constant c so that every semicomplete digraph of minimum out-degree at least 2k+ck has such a partition. This is tight up to the value of c.
A polynomial time solution algorithm is described to find a smallest subset R of nodes of a directed graph D = (V, A) such that, for every node v is an element of V - R, there are k edge-disjoint paths from R to v and...
详细信息
A polynomial time solution algorithm is described to find a smallest subset R of nodes of a directed graph D = (V, A) such that, for every node v is an element of V - R, there are k edge-disjoint paths from R to v and there are / edge-disjoint paths from v to R. (C) 2004 Elsevier B.V. All rights reserved.
Stiebitz [Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321-324] proved that if every vertex v in a graph G has degree d (v) >= a (v) + b(v) + I (where a and b are arbitrarily given nonnega...
详细信息
Stiebitz [Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321-324] proved that if every vertex v in a graph G has degree d (v) >= a (v) + b(v) + I (where a and b are arbitrarily given nonnegative integer-valued functions) then G has a nontrivial vertex partition (A, B) such that d(A) (v) >= a (v) for every v is an element of A and d(B) (v) >= b(v) for every v is an element of B. Kaneko [On decomposition of triangle-free graphs under degree constraints, J. Graph Theory 27 (1998) 7-91 and Diwan [Decomposing graphs with girth at least five under degree constraints, J. Graph Theory 33 (2000) 237-239] strengthened this result, proving that it suffices to assume d(v) >= a + b (a, b >= 1) or just d(v) >= a + b - 1 (a, b >= 2) if G contains no cycles shorter than 4 or 5, respectively. The original proofs contain nonconstructive steps. In this paper we give polynomial-time algorithms that find such partitions. Constructive general izati ons for k-partitions are also presented. (c) 2006 Elsevier B.V. All rights reserved.
暂无评论