A graph has the neighbor-closed-co-neighbor, or ncc property, if for each of its vertices x, the subgraph induced by the neighbor set of x is isomorphic to the subgraph induced by the closed non-neighbor set of x. As ...
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A graph has the neighbor-closed-co-neighbor, or ncc property, if for each of its vertices x, the subgraph induced by the neighbor set of x is isomorphic to the subgraph induced by the closed non-neighbor set of x. As proved by Bonato and Nowakowski [5], graphs with the ncc property are characterized by the existence of perfect matchings satisfying certain local conditions. In the present article, we investigate the spanning subgraphs of ncc graphs, which we name sub-ncc. Several equivalent characterizations of finite sub-ncc graphs are given, along with a polynomial time algorithm for their recognition. The infinite sub-ncc graphs are characterized, and we demonstrate the existence of a countable universal sub-ncc graph satisfying a strong symmetry condition called pseudo-homogeneity. (c) 2005 Wiley Periodicals, Inc.
We consider the following network design problem that we call the Generalized Terminal Backup Problem: given a graph (or a hypergraph) G(0) = (V, E-0), a set of (at least 2) terminals T subset of V, and a requirement ...
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We consider the following network design problem that we call the Generalized Terminal Backup Problem: given a graph (or a hypergraph) G(0) = (V, E-0), a set of (at least 2) terminals T subset of V, and a requirement r(t) for every t is an element of T, find a multigraph G = (V, E) such that lambda G(0)+ G(t, T - t) >= r(t) for any t is an element of T. In the minimum cost version the objective is to find G minimizing the total cost c(E) = Sigma(uv is an element of E) c(uv), given also costs c(uv) >= 0 for every pair u, v is an element of V. In the degree-specified version the question is to decide whether such a G exists, satisfying that the degree of v is an element of V is a prescribed value m(v). The Terminal Backup Problem solved in [E. Anshelevich and A. Karagiozova, SIAM J. Comput., 40 (2011), pp. 678-708] is the special case where G(0) is the empty graph and r(t) = 1 for every terminal t is an element of T. We solve the Generalized Terminal Backup Problem in the following two cases. In the first case we solve the degree-specified version by a splitting-off theorem. This splitting-off theorem in turn provides the solution for the minimum cost version in the case when c is node-induced, that is c(uv) = w(u) + w(v) for some node weights w : V -> R+. In the second case we turn to the general minimum cost version, and we are able to solve it when G0 is the empty graph. This includes the Terminal Backup Problem (r = 1) and the Maximum-Weight b-matching Problem (T = V). The solution depends on an interesting new variant of a theorem of Lovasz and Cherkassky, and on the solution of the so-called Simplex Matching Problem. Our algorithms run in polynomialtime for both problems.
We extend congestion games to the setting where players need to make multiple joint choices with interactions in a hierarchical manner (termed joint congestion game). At each choice dimension, players are involved in ...
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We extend congestion games to the setting where players need to make multiple joint choices with interactions in a hierarchical manner (termed joint congestion game). At each choice dimension, players are involved in a typical congestion game. This game has a feature that the output of one choice dimension serves as an input of another one, and the costs paid by players in different choice dimensions are interdependent. Focusing on the joint congestion game with destination and route choices (i.e., select which destination and which route to complete a trip), we show the existence and uniqueness of the Nash equilibrium under mild assumptions in a nonatomic game setting. Then we investigate the property of the general quantal response equilibrium (QRE) for the joint congestion game in which players have perception errors of their costs (characterized by a probabilistic distribution). The QRE condition for the joint congestion game is further extended to the case where the analyst has only incomplete information about players' perceived costs. A specific cross moment QRE model using the mean and covariance information is accordingly developed to account for both the analyst's and players' imperfect information/perception. We present an equivalent convex program that promises a unique solution for the cross moment QRE model, and provide a polynomialalgorithm to solve it. Numerical results illustrate the features of the developed model for the joint congestion game and demonstrate the efficiency of the solution algorithm on two realistic transportation networks.
We determine the computational complexity of deciding whether m polynomials in n variables have relatively prime leading terms with respect to some term order. This problem in NP-complete in general, but solvable in p...
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We determine the computational complexity of deciding whether m polynomials in n variables have relatively prime leading terms with respect to some term order. This problem in NP-complete in general, but solvable in polynomialtime in two different situations, when m is fixed and when n - m is fixed. Our new algorithm for the second case determines a candidate set of leading terms by solving a maximum matching problem. This reduces the problem to linear programming.
A cycle C in a graph G is extendable if there is some other cycle in G that contains each vertex of C plus one additional vertex. A graph is cycle extendable if every non-Hamilton cycle in the graph is extendable. A b...
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A cycle C in a graph G is extendable if there is some other cycle in G that contains each vertex of C plus one additional vertex. A graph is cycle extendable if every non-Hamilton cycle in the graph is extendable. A balanced incomplete block design, BIBD(v,k,), consists of a set V of v elements and a block set B of k-subsets of V such that each 2-subset of V occurs in exactly of the blocks of B. The block-intersection graph of a design D=(V,B) is the graph GD having B as its vertex set and such that two vertices of GD are adjacent if and only if their corresponding blocks have nonempty intersection. In this paper, we prove that the block-intersection graph of any BIBD(v,k,) is cycle extendable. Furthermore, we present a polynomial time algorithm for constructing cycles of all possible lengths in a block-intersection graph. (C) 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 303-310, 2013
The virtual path (VP) concept is known to be a powerful transport mechanism for ATM networks. This paper deals with the optimization of the virtual paths system from a bandwidth utilization perspective. While previous...
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The virtual path (VP) concept is known to be a powerful transport mechanism for ATM networks. This paper deals with the optimization of the virtual paths system from a bandwidth utilization perspective. While previous research on VP management has basically assumed that bandwidth in ATM networks is unlimited, emerging technologies and applications are changing this premise. In many networks, such as wireless, bandwidth is always at a premium. In wired networks, with increasing user access speeds, less than a dozen of broadband connections can saturate even a Gigabit link. In this paper we present an efficient algorithm that finds a system of VP routes for a given set of VP terminators and VP capacity demands. This solution is motivated by the need to minimize the load, or reduce congestion, generated by the VP's on individual links. A nontrivial performance guarantee is proven for the quality of the proposed solution and numerical results show that the proposed solution carries the potential for a near optimal allocation of VP's.
While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-f...
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While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-free matching, which is a relaxation of a stable matching preserving a kind of fairness property. In this paper, we investigate the existence of an envy-free matching in several settings, in which hospitals have lower quotas and not all doctor-hospital pairs are acceptable. We first provide an algorithm that decides whether a given HR-LQ instance has an envy-free matching or not. Then, we consider envy-freeness in the Classified Stable Matching model due to Huang (in: Procedings of 21st annual ACM-SIAM symposium on discrete algorithms (SODA2010), SIAM, Philadelphia, pp 1235-1253, 2010), i.e., each hospital has lower and upper quotas on subsets of doctors. We show that, for this model, deciding the existence of an envy-free matching is NP-hard in general, but solvable in polynomialtime if quotas are paramodular.
This paper studies single vehicle scheduling problems with two agents on a line-shaped network. Each of two agents has some customers that are situated at some vertices on the network. A vehicle has to start from upsi...
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This paper studies single vehicle scheduling problems with two agents on a line-shaped network. Each of two agents has some customers that are situated at some vertices on the network. A vehicle has to start from upsilon(0) to serve all customers. The objective is to schedule the customers to minimize C-max(A) + theta C-max(B), where C-max(X) is the latest completion time of the customers for agent X and X is an element of{A,B}. We first propose a polynomial time algorithm for the problem without release time. Next, the problem with release time is proved to be NP-hard despite of a network with only two vertices. Then, we present a 3+root 5/2 -approximation algorithm. Finally, numerical experiments are carried out to verify the approximation algorithm is effective.
In this paper a one-machine scheduling model is analyzed where n different jobs are classified into K groups depending on which additional resource they require. The change-over time from one job to another consists o...
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In this paper a one-machine scheduling model is analyzed where n different jobs are classified into K groups depending on which additional resource they require. The change-over time from one job to another consists of the removal time or of the set-up time of the two jobs. It is sequence-dependent in the sense that the change-over time is determined by whether or not the two jobs belong to the same group. The objective is to minimize the make pan. This problem can be modeled as an asymmetric Traveling Salesman Problem (TSP) wit? a specially structured distance matrix. For this problem we give a polynomialtime solution algorithm that runs in O(nlogn) time. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
In this paper we give a new convergence analysis of a projective scaling algorithm. We consider a long-step affine scaling algorithm applied to a homogeneous linear programming problem obtained from the original linea...
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In this paper we give a new convergence analysis of a projective scaling algorithm. We consider a long-step affine scaling algorithm applied to a homogeneous linear programming problem obtained from the original linear programming problem. This algorithm takes a fixed lambda less than or equal to 2/3 of the way towards the boundary of the nonnegative orthant at each iteration. The iteration sequence for the original problem is obtained by pulling back the homogeneous iterates onto the original feasible region with a conical projection, which generates the same search direction as the original projective scaling algorithm at each iterate. The recent convergence results for the long-step affine scaling algorithm by the authors are applied to this algorithm to obtain some convergence results on the projective scaling algorithm. Specifically, we will show (i) polynomiality of the algorithm with complexities of O(nL) and O(n(2)L) iterations for lambda < 2/3 and lambda = 2/3, respectively;(ii) global convergence of the algorithm when the optimal face is unbounded;(iii) convergence of the primal iterates to a relative interior point of the optimal face;(iv) convergence of the dual estimates to the analytic center of the dual optimal face;and (v) convergence of the reduction rate of the objective function value to 1 - lambda.
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