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approximation algorithms for MAX RES CUT with limited unbalanced constraints

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2010年第1-2期33卷 357-374页

作者： Ling, Aifan Tang, Le Xu, Chengxian Jiangxi Univ Finance & Econ Sch Finance Nanchang 330013 Jiangxi Peoples R China Jiangxi Blue Sky Univ Nanchang 330098 Jiangxi Peoples R China Xi An Jiao Tong Univ SKLMSE Lab Xian 710049 Peoples R China Xi An Jiao Tong Univ Dept Sci Comp & Appl Software Xian 710049 Peoples R China

Two kinds of MAX RES CUT problems, the MAX s - t CUT and the MAX s - t - v CUT, with limited unbalanced constraints are considered. approximation algorithms used in Frieze and Jerrum (Integer Programming and Combinatorial Optimization, vol. 920, pp. 1-13, Springer, Berlin, 1995), Galbiati and Maffioli (Theor. Comput. Sci. 385: 78-87, 2007), Han et al. (Math. Program. Ser. B 92: 509535, 2002) and Ye (Math. Programm. 90: 101-111, 2001) are extended to the two MAX RES CUT problems. A special matrix P is constructed by which it can ensure that the given nodes s, t are feasible to equality constraints with probability one for theMAX s - t CUT and s, t, v are feasible to equality constraints with at least probability 0.912 for the MAX s - t - v CUT. A fussy greedy sizing-adjusted procedure is then proposed to confirm that the round solution is feasible for all constraints. We find these extensions are nontrivial and some interesting results about performance ratio are obtained for the MAX RES CUT problem with limited unbalanced constraints.

关键词： MAX RES CUT Limited unbalanced constraints approximation algorithm Semidefinite programming relaxation

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CONSTRAINED RELAY NODE DEPLOYMENT FOR UNDERWATER ACOUSTIC WIRELESS SENSOR NETWORKS

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DISCRETE MATHEMATICS algorithmS AND APPLICATIONS 2012年第1期4卷

作者： Li, Deying Li, Zheng Chen, Wenping Renmin Univ China Sch Informat MOE Key Lab Data Engn & Knowledge Engn Beijing Peoples R China

An underwater acoustic wireless sensor network (UA-WSN) consists of many resourceconstrained underwater sensor nodes (USNs), which are deployed to perform collaborative monitoring tasks over a given region. One way to preserve network connectivity while guaranteeing other network QoS is to deploy some relay nodes (RNs) in the networks. Although RNs' function is more powerful than USNs, but they can lead to more interference and their cost is more expensive. This paper addresses constrained low-interference relay node deployment problem for 3-D UA-WSNs in which the RNs are placed at a subset of candidate locations to ensure connectivity between the USNs such that the number of RNs deployed and the value of total incremental interference are minimized. We first prove that it is NP-hard, then propose a general approximation algorithm framework. Based on the framework, we get two polynomial time O(1)-approximation algorithms.

关键词： Underwater acoustic wireless sensor network relay node deployment connectivity low-interference approximation algorithm

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approximation algorithms for shortest descending paths in terrains

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JOURNAL OF DISCRETE algorithmS 2010年第2期8卷 214-230页

作者： Ahmed, Mustaq Das, Sandip Lodha, Sachin Lubiw, Anna Maheshwari, Anil Roy, Sasanka Univ Waterloo David R Cheriton Sch Comp Sci Waterloo ON N2L 3G1 Canada Indian Stat Inst Kolkata India Tata Consultancy Serv Ltd Pune Maharashtra India Carleton Univ Sch Comp Sci Ottawa ON K1S 5B6 Canada

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a polyhedral terrain. We present two approximation algorithms that solve the SDP problem on general terrains. We also introduce a generalization of the shortest descending path problem, called the shortest gently descending path (SGDP) problem, where a path descends, but not too steeply. The additional constraint to disallow a very steep descent makes the paths more realistic in practice. We present two approximation algorithms to solve the SGDP problem on general terrains. All of our algorithms are simple, robust and easy to implement. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Descending path Gently descending path Shortest path approximation algorithm Terrain Computational geometry

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CONFLICT-AWARE DATA AGGREGATION SCHEDULING IN WIRELESS SENSOR NETWORKS WITH ADJUSTABLE TRANSMISSION RANGE

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DISCRETE MATHEMATICS algorithmS AND APPLICATIONS 2012年第3期4卷

作者： Hong, Yi Du, Hongwei Li, Deying Chen, Wenping Renmin Univ China Sch Informat Beijing 100872 Peoples R China Harbin Inst Technol Dept Comp Sci & Technol Shenzhen Grad Sch Shenzhen Shenzhen 518055 Peoples R China

The minimum latency data aggregation schedule is one of the fundamental problems in wireless sensor networks. Most existing works assumed that the transmission ranges of sensor nodes cannot be adjusted. However, sensors with adjustable transmission ranges have advantages in energy saving, reducing transmission interference and latency. In this paper, we study the minimum latency conflict-aware data aggregation scheduling problem with adjustable transmission radii: given locations of sensors along with a base station, all sensors could adjust their transmission radii and each sensor's interference radius is a times of its transmission radius, we try to find a data aggregation schedule in which the data from all sensors can be transmitted to the base station without conflicts, such that the latency is minimized. We first partition the set of all nodes into two parts: the major set and the minor set. Then, we design different scheduling strategies for the two sets, respectively. Finally, we propose an approximation algorithm for the problem and prove the performance ratio of the algorithm is bounded by a nearly constant. Our experimental results evaluate the efficiency of the proposed algorithm.

关键词： Latency data aggregation wireless sensor network conflict-aware approximation algorithm

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approximation algorithms for homogeneous polynomial optimization with quadratic constraints

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MATHEMATICAL PROGRAMMING 2010年第2期125卷 353-383页

作者： He, Simai Li, Zhening Zhang, Shuzhong Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China City Univ Hong Kong Dept Management Sci Kowloon Tong Hong Kong Peoples R China

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids;namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied.

关键词： Multi-linear tensor form Polynomial function optimization approximation algorithm

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approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth

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JOURNAL OF THE ACM 2011年第5期58卷 1–37页

作者： Bateni, Mohammadhossein Hajiaghayi, Mohammadtaghi Marx, Daniel Princeton Univ Dept Comp Sci Princeton NJ 08540 USA Univ Maryland Dept Comp Sci College Pk MD 20742 USA Humboldt Univ Inst Informat D-10099 Berlin Germany Ctr Computat Intractabil Princeton NJ USA

We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, we show how to build a Steiner forest spanner for such graphs. The crux of the process is a clustering procedure called prize-collecting clustering that breaks down the input instance into separate subinstances which are easier to handle;moreover, the terminals in different subinstances are far from each other. Each subinstance has a relatively inexpensive Steiner tree connecting all its terminals, and the subinstances can be solved (almost) separately. Another building block is a PTAS for Steiner forest on graphs of bounded treewidth. Surprisingly, Steiner forest is NP-hard even on graphs of treewidth 3. Therefore, our PTAS for bounded-treewidth graphs needs a nontrivial combination of approximation arguments and dynamic programming on the tree decomposition. We further show that Steiner forest can be solved in polynomial time for series-parallel graphs (graphs of treewidth at most two) by a novel combination of dynamic programming and minimum cut computations, completing our thorough complexity study of Steiner forest in the range of bounded-treewidth graphs, planar graphs, and bounded-genus graphs.

关键词： algorithms Design Performance Theory approximation algorithm bounded-treewidth dynamic programming network design planar graph PTAS series-parallel graph Steiner forest

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Single-Vehicle Scheduling Problems with Release and Service Times on a Line

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NETWORKS 2011年第2期57卷 128-134页

作者： Yu, Wei Liu, Zhaohui E China Univ Sci & Technol Dept Math Shanghai 200237 Peoples R China

We consider the following vehicle scheduling problem. There are some customers on a line that will be served by a single vehicle. Each customer is associated with a release time and a service time. The objective is to schedule the vehicle to minimize the makespan. For the tour version, where the makespan means the time when the vehicle has served all customers and returned back to its initial location, we present a 3/2-approximation algorithm. For the path version, where the makespan is defined as the time by which the last customer has been served completely, we present a 5/3-approximation algorithm. (C) 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(2), 128-134 2011

关键词： vehicle routing vehicle scheduling approximation algorithm

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approximation algorithm for base station placement in wireless sensor networks

Approximation algorithm for base station placement in wirele...

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4th Annual IEEE-Communications-Society Conference on Sensor, Mesh and AD HOC Communications and Networks

作者： Shi, Yi Hou, Y. Thomas Virginia Tech Bradley Dept Elect & Comp Engn Blacksburg VA 24061 USA

ISBN: (纸本)9781424412679

Base station location has significant impact on network lifetime performance for a sensor network. For a multi-hop sensor network, this problem is particular challenging as we need to jointly consider base station placement and data routing strategy to maximize network lifetime performance. This paper presents an approximation algorithm that can guarantee (1 - epsilon) optimal network lifetime performance for base station placement problem with any desired error bound epsilon > 0. The proposed (1 - epsilon) optimal approximation algorithm is based on several novel techniques that enable to reduce an infinite search space to a finite-element search space for base station location. The first technique used in this reduction is to discretize cost parameters (with performance guarantee) associated with energy consumption. Subsequently, the continuous search space can be broken up into a finite number of subareas. The second technique is to exploit the cost property of each subarea and represent it by a novel notion called "fictitious cost point," each with guaranteed cost bounds. This approximation algorithm offers a simpler and in most cases practically faster algorithm than a state-of-the-art algorithm and represents the best known result to this important problem.

关键词： theory approximation algorithm base station placement network lifetime sensor network

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A Fully Polynomial approximation Scheme for a Knapsack Problem with a Minimum Filling Constraint (Extended Abstract)

A Fully Polynomial Approximation Scheme for a Knapsack Probl...

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12th algorithms and Data Structures Symposium (WADS 2011)

作者： Xu, Zhou Lai, Xiaofan Hong Kong Polytech Univ Fac Business Dept Logist & Maritime Studies Kowloon Hong Kong Peoples R China

ISBN: (纸本)9783642222993

We study a variant of the knapsack problem, where a minimum filling constraint is imposed such that the total weight of selected items cannot be less than a given threshold. We consider the case when the ratio of the threshold to the capacity equals a given constant alpha with 0 <= alpha <= 1. For any such constant alpha, since finding an optimal solution is NP-hard, we develop the first FPTAS for the problem, which has a time complexity polynomial in 1/(1 - alpha).

关键词： approximation algorithm FPTAS knapsack problem minimum filling constraint

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approximation algorithms for homogeneous polynomial optimization with quadratic constraints

Approximation algorithms for homogeneous polynomial optimiza...

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20th International Symposium of Mathematical Programming (ISMP)

关键词： Multi-linear tensor form Polynomial function optimization approximation algorithm

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