When facilities are built to serve end consumers directly, it is natural that consumer demands are affected by the number of open facilities. Moreover, sometimes a facility becomes more attractive if other facilities ...
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When facilities are built to serve end consumers directly, it is natural that consumer demands are affected by the number of open facilities. Moreover, sometimes a facility becomes more attractive if other facilities around it are built. To capture these factors, in this study we construct a discrete location model for profit maximization with endogenous consumer demands and network effects. The effective demand is then a concave function of the sum of benefits of open facilities due to the diminishing marginal benefit effect. When the function is linear, we design a polynomial-time algorithm to find an optimal solution. When it is nonlinear, we show that the problem is NP-hard and develop an approximation algorithm based on demand function approximation, linear relaxation, decomposition, and sorting. It is demonstrated that the proposed algorithm has worst-case performance guarantees for some special cases of our problem. Numerical studies are conducted to demonstrate the average performance and general applicability of our algorithms. (C) 2017 Elsevier B.V. All rights reserved.
We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph...
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We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph H = （V, E） into two subsets V1, V2 with ｜｜V2｜ - ｜1/1 ｜｜ ≤ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance （MC-LU）, Max Set Splitting, Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/｜V｜. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko （2000） on Max Hypergraph Bisection （MHC-LU with u = 0）, and results of Andersson and Engebretsen （1999）, Gaur and Krishnamurti （2001） and Zhang et al. （2004） on Max Set Splitting （MHC-LU with u = ｜V｜）. Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli （2007） is responsible for the improvement of a result of Galbiati and Maffioli （2007） on MC-LU for some range of τ.
In this paper, we consider the stochastic facility location problem with submodular penalties. By exploring the structural properties of submodular function, we present a primal-dual -approximation algorithm for the p...
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In this paper, we consider the stochastic facility location problem with submodular penalties. By exploring the structural properties of submodular function, we present a primal-dual -approximation algorithm for the problem.
We formulate a multi-directional broadcast (MDB) storm problem arising in dense vehicular ad-hoc networks (VANETs) when the multiple nodes (moving in multiple directions) forward broadcast packets meet at the road int...
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We formulate a multi-directional broadcast (MDB) storm problem arising in dense vehicular ad-hoc networks (VANETs) when the multiple nodes (moving in multiple directions) forward broadcast packets meet at the road intersections, resulting in severe packet collisions inducing delays at medium access control. In this work, we have proposed a mechanism for partitioning the graph of vehicles in an intersection into multiple bipartite directional sub-graphs, such that each sub-graph aggregates messages using short range communication and make one long range communication of aggregated message. The k balanced graph partitioning problem contains partitions of size <= vertical bar V vertical bar/k nodes. For a graph G = (V, E), a partitioning P, is (k, 1 + epsilon) balanced if V is partitioned into k disjoint subsets each containing at most (1 + epsilon)n/k vertices. Our proposed approximation algorithm for intersection-cast problem uses a balanced partition with Theta (log<^>2 n) approximation for balance constant, v > 1. We have given simulation results for the performance analysis of our intersection-cast protocol compared to the existing competitive schemes and found improvement in terms of broadcast success rate, reachability and message overhead in the networks.
We consider the stochastic version of the facility location problem with service installation costs. Using the primal-dual technique, we obtain a 7-approximation algorithm.
We consider the stochastic version of the facility location problem with service installation costs. Using the primal-dual technique, we obtain a 7-approximation algorithm.
This Paper deals with the allocation of records on a linear storage device to minimize the average access time when the request probabilities to the recores are not independent. For sequential access, algorithms to ob...
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This Paper deals with the allocation of records on a linear storage device to minimize the average access time when the request probabilities to the recores are not independent. For sequential access, algorithms to obtain optimal and approximate solutions are presented. The approximation algorithm is also used with little modification for direct access. The performance of the approximation algorithm is estimated.
In this paper,we study a stochastic version of the fault-tolerant facility location *** exploiting the stochastic structure,we propose a 5-approximation algorithm which uses the LP-rounding technique based on the revi...
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In this paper,we study a stochastic version of the fault-tolerant facility location *** exploiting the stochastic structure,we propose a 5-approximation algorithm which uses the LP-rounding technique based on the revised optimal solution to the linear programming relaxation of the stochastic fault-tolerant facility location problem.
In this paper,we consider the risk-adjusted two-stage stochastic facility location problem with penalties(RSFLPP).Using the monotonicity and positive homogeneity of the risk measure function,we present an LP-roundin...
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In this paper,we consider the risk-adjusted two-stage stochastic facility location problem with penalties(RSFLPP).Using the monotonicity and positive homogeneity of the risk measure function,we present an LP-rounding-based 6-approximation algorithm.
We present an approximation algorithm for solving graph problems in which a low-cost set of edges must be selected that has certain vertex-connectivity properties. In the survivable network design problem, a value r(i...
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We present an approximation algorithm for solving graph problems in which a low-cost set of edges must be selected that has certain vertex-connectivity properties. In the survivable network design problem, a value r(ij) for each pair of vertices i and j is given, and a minimum-cost set of edges such that there are r(ij) vertex-disjoint paths between vertices i and j must be found. In the case for which r(ij) is an element of (0, 1, 2) for all i, j, we can find a solution of cost no more than three times the optimal cost in polynomial time. In the case in which r(ij) = k for all i, j, we can find a solution of cost no more than 2H(k) times optimal, where H(n) = 1 + 1/2 + ... + 1/n. No approximation algorithms were previously known for these problems. Our algorithms rely on a primal-dual approach which has recently led to approximation algorithms for many edge-connectivity problems.
A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the fi...
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A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an approximation algorithm with a constant approximation ratio. In addition, the proposed algorithm yields a solution that meets both the no-repeater and mirrored constraints. Computational experiments show that the algorithm generates solutions of good quality.
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