Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design

Jothi, Raja; Raghavachari, Balaji

doi:10.1145/1103963.1103967

Cited by 41 publications

(14 citation statements)

References 38 publications

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“…For example the Degree-Constrained MST problem (Pagacz, 2006), Bounded Diameter MST problem formulated by Nghia and Binh (Nghia, 2008), and the Capacitated Minimum Spanning Tree problem (Jothi, 2005 andZhou, 2006). Many computationally efficient algorithms have been developed by many researchers (Gen M, 2000, Oncan, 2007, SalazarNeumann, 2007and Zhou, 1998 for the solution of deterministic MST problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Development of Gis Tool for the Solution of Minimum Spanning Tree Problem using Prim's Algorithm

Dutta¹,

Patra²,

Shankar

et al. 2014

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:A minimum spanning tree (MST) of a connected, undirected and weighted network is a tree of that network consisting of all its nodes and the sum of weights of all its edges is minimum among all such possible spanning trees of the same network. In this study, we have developed a new GIS tool using most commonly known rudimentary algorithm called Prim's algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network. This algorithm is based on the weight (adjacency) matrix of a weighted network and helps to solve complex network MST problem easily, efficiently and effectively. The selection of the appropriate algorithm is very essential otherwise it will be very hard to get an optimal result. In case of Road Transportation Network, it is very essential to find the optimal results by considering all the necessary points based on cost factor (time or distance). This paper is based on solving the Minimum Spanning Tree (MST) problem of a road network by finding it's minimum span by considering all the important network junction point. GIS technology is usually used to solve the network related problems like the optimal path problem, travelling salesman problem, vehicle routing problems, location-allocation problems etc. Therefore, in this study we have developed a customized GIS tool using Python script in ArcGIS software for the solution of MST problem for a Road Transportation Network of Dehradun city by considering distance and time as the impedance (cost) factors. It has a number of advantages like the users do not need a greater knowledge of the subject as the tool is user-friendly and that allows to access information varied and adapted the needs of the users. This GIS tool for MST can be applied for a nationwide plan called Prime Minister Gram Sadak Yojana in India to provide optimal all weather road connectivity to unconnected villages (points). This tool is also useful for constructing highways or railways spanning several cities optimally or connecting all cities with minimum total road length.

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Section: Literature Reviewmentioning

confidence: 99%

Development of Gis Tool for the Solution of Minimum Spanning Tree Problem using Prim's Algorithm

Dutta¹,

Patra²,

Shankar

et al. 2014

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…This problem can be reduced from the Capacitated Minimum Spanning Tree Problem (CM-STP) [14], by assigning each edge with weight 1 and assuming Q to be the cardinality constraint on the number of nodes in any subtree. The CMSTP is known to be NP-hard when 3 ≤ Q ≤ n 2 [12].…”

Section: Preliminariesmentioning

confidence: 99%

Data quality maximization in sensor networks with a mobile sink

Liang

Wark

2011

2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS)

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Abstract-In this paper we consider a wireless sensor network with a mobile sink moving along a fixed trajectory without stop to collect data. We assume that a few powerful and highcapacity sensors deployed nearby the trajectory are the gateways, which are able to communicate with the sink directly when the sink is within their transmission ranges. Gateways play the role of relay nodes for the other sensors in the network. We also assume that the time of data uploading from the gateways to the mobile sink is limited. Thus, data from only a subset of sensors, called packet nodes, can be collected and used to estimate those of the others. The data quality is measured by the estimation accuracy. The upper bound on the number of packet nodes for a gateway is defined as the gateway quota. We formulate the optimization problem with the objective to identify the set of packet nodes, allocate them to gateways subject to gateway quotas, and devise an energy-efficient routing protocol, such that the sink can efficiently collect data generated from packet nodes with the maximum quality. Due to the NP-hardness of this problem, we propose a heuristic with low computation complexity. We also conduct extensive experiments by simulation to evaluate the performance of the proposed heuristic.

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“…Also given as input are a capacity constraint k, and root vertex r ∈ V . The extensively studied capacitated minimum spanning tree (CMST) problem [4,10,17] asks for a minimum cost spanning tree rooted at r in which the sum of the vertex weights in every subtree (local access network) hanging off r is at most k. The problem is feasible only when k is at least as much as the largest vertex weight. The CMST problem is NP-hard [13].…”

Section: Introductionmentioning

confidence: 99%