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Minimum Color-spanning Tree
, M.Sc. Thesis Sharif University of Technology ; Abam, Mohammad Ali (Supervisor)
Abstract
In the general case of minimum color-spanning tree which is one of the color-spanning set problems, given a weighted graph with n vertices of k different colors, the goal is to find a subtree of minimum weight such that vertices of this subtree include all the colors in the graph. In the planar case, the input is a complete graph with n colored vertices on the plane and the weight of each edge is the Euclidean distance between its corresponding vertices. In this thesis we consider the problem of minimum color-spanning tree. To this end, first we present various color-spanning set problems and some other related problems like Steiner tree and we study the previous work on these problems. Then...
Unit covering in color-spanning set model
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 26 February 2015 through 28 February 2015 ; Volume 8973 , February , 2015 , Pages 44-52 ; 03029743 (ISSN) ; 9783319156118 (ISBN) ; Ghodsi, M ; Homapour, H ; Seddighin, M ; Sharif University of Technology
Springer Verlag
2015
Abstract
In this paper, we consider two new variants of the unit covering problem in color-spanning set model: Given a set of n points in d-dimensional plane colored with m colors, the MinCSBC problem is to select m points of different colors minimizing the minimum number of unit balls needed to cover them. Similarly, the MaxCSBC problem is to choose one point of each color to maximize the minimum number of needed unit balls. We show that MinCSBC is NP-hard and hard to approximate within any constant factor even in one dimension. For d = 1, however, we propose an ln(m)-approximation algorithm and present a constant-factor approximation algorithm for fixed f, where f is the maximum frequency of the...