We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset...
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We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of 2 and mi...
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We consider the fundamental problem of scheduling data mules for managing a wireless sensor network. A data mule tours around a sensor network and can help with network maintenance such as data collection and battery ...
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We study problems that integrate buy-at-bulk network design into the classical (connected) facility location problem. In such problems, we need to open facilities, build a routing network, and route every client deman...
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We are given a set of items, and a set of knapsacks. Both the weight and the profit of an item are functions of the knapsack, and each knapsack has a positive real capacity. A restriction is setting that the number of...
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ISBN:
(纸本)9781479986477
We are given a set of items, and a set of knapsacks. Both the weight and the profit of an item are functions of the knapsack, and each knapsack has a positive real capacity. A restriction is setting that the number of the items which are admissible to each knapsack is no more than k, and these items are taken as input for each knapsack. We consider two following objectives: (1) maximizing the total profit of all the knapsacks (Max-Sum k-GMK), (2) maximizing the minimum profit of all the knapsacks (Max-Min k-GMK). We show that the two problems are NP-complete when k is greater than or equal to 4. For the Max-Sum k-GMK problem, we can obtain a 1/2-approximation algorithm, and especially when k=2, we design an optimal algorithm. For the Max-Min k-GMK problem, we present a 1/ (k-1)-approximation algorithm, and especially when k=2, this algorithm is an optimal algorithm.
In this paper, we develop approximation algorithms for a few node deletion problems when the input is restricted to be a bipartite graph. We look at node deletion problems for non-trivial properties which can be chara...
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In this paper, we develop approximation algorithms for a few node deletion problems when the input is restricted to be a bipartite graph. We look at node deletion problems for non-trivial properties which can be characterized by forbidden structure which has a bounded intersection with both the bipartitions. The approximation factors obtained directly depend upon the size of the largest such intersection. Special instances of this general problem include problems such as the MINIMUM CHAIN VERTEX DELETION, MINIMUM DISSOCIATION VERTEX DELETION, MINIMUM BIPARTITE CLAW VERTEX DELETION, MINIMUM BI-COMPLEMENT VERTEX DELETION and MINIMUM BIPARTITE THRESHOLD VERTEX DELETION problems. The algorithms are based upon the techniques of linear programming and iterative rounding. We also use the node deletion algorithms to marginally improve the trivial approximation factor for complementary problem of determining the size of the maximum sized vertex induced subgraph lying in the given graph class and prove the APX-completeness of all of these problems. (C) 2014 Elsevier B.V. All rights reserved.
We develop the first approximation algorithm with worst-case performance guarantee for capacitated stochastic periodic-review inventory systems with setup costs. The structure of the optimal control policy for such sy...
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We develop the first approximation algorithm with worst-case performance guarantee for capacitated stochastic periodic-review inventory systems with setup costs. The structure of the optimal control policy for such systems is extremely complicated, and indeed, only some partial characterization is available. Thus, finding provably near-optimal control policies has been an open challenge. In this article, we construct computationally efficient approximate optimal policies for these systems whose demands can be nonstationary and/or correlated over time, and show that these policies have a worst-case performance guarantee of 4. We demonstrate through extensive numerical studies that the policies empirically perform well, and they are significantly better than the theoretical worst-case guarantees. We also extend the analyses and results to the case with batch ordering constraints, where the order size has to be an integer multiple of a base load. (C) 2014 Wiley Periodicals, Inc.
The ring loading problem and its variants have been extensively studied in the last fifteen years, under the assumption that all requests have to be satisfied. However, in many practical cases, one may wish to reject ...
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The ring loading problem and its variants have been extensively studied in the last fifteen years, under the assumption that all requests have to be satisfied. However, in many practical cases, one may wish to reject some requests, which results in a penalty cost. We introduce the ring loading problem with penalty cost, which generalizes the well-known ring loading problem (Schrijver et al., 1999 [14]). We prove that this problem is NP-hard even if the demand can be split, and design a 1.58-approximation algorithm for the integer demand splittable case and a (1.58 + epsilon)-approximation algorithm for the demand unsplittable case, for any given number epsilon > 0. (C) 2013 Elsevier B.V. All rights reserved.
This work deals with the continuous time lot-sizing inventory problem when demand and costs are time-dependent. We adapt a cost balancing technique developed for the periodic-review version of our problem to the conti...
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This work deals with the continuous time lot-sizing inventory problem when demand and costs are time-dependent. We adapt a cost balancing technique developed for the periodic-review version of our problem to the continuous-review framework. We prove that the solution obtained costs at most twice the cost of an optimal solution. We study the numerical complexity of the algorithm and generalize the policy to several important extensions while preserving its performance guarantee of two. Finally, we propose a modified version of our algorithm for the lot-sizing model with some restricted settings that improves the worst-case bound. (C) 2013 Elsevier B.V. All rights reserved.
Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying th...
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Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into served clients, paying the transportation cost to serve them. We give polynomial-time reductions from this problem and variants to the (un)capacitated facility location problem, directly yielding approximation algorithms, two with constant factors in the metric case, one with a logarithmic factor in the general case. Published by Elsevier B.V.
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