Color spanning objects: algorithms and hardness results

Show simple item record Banerjee, Sandip Misra, Neeldhara Nandy, Subhas C. 2018-04-10T10:04:18Z 2018-04-10T10:04:18Z 2018-03
dc.identifier.citation Banerjee, Sandip; Misra, Neeldhara and Nandy, Subhas C., “Color spanning objects:algorithms and hardness results”, Discrete Applied Mathematics, DOI: 10.1016/j.dam.2018.02.014, vol. 280, pp. 14-22, Mar. 2018. en_US
dc.identifier.issn 0166-218X
dc.description.abstract In this paper, we study the Shortest Color Spanning - Intervals problem, and related generalizations, namely Smallest Color Spanning - Squares and Smallest Color Spanning - Circles. The generic setting is the following: we are given points in the plane (or on a line), each colored with one of colors. For each color we also have a demand . Given a budget , we are required to find at most objects (for example, intervals, squares, circles, etc.) that cover at least points of color . Typically, the goal is to minimize the maximum perimeter or area. We provide exact algorithms for these problems for the cases of intervals, circles and squares, generalizing several known results. In the case of intervals, we provide a comprehensive understanding of the complexity landscape of the problem after taking several natural parameters into account. Given that the problem turns out to be -hard parameterized by the standard parameters, we introduce a new parameter, namely sparsity, and prove new hardness and tractability results in this context. For squares and circles, we use existing algorithms of one smallest color spanning object in order to design algorithms for getting identical objects of minimum size whose union spans all the colors.
dc.description.statementofresponsibility by Sandip Banerjee, Neeldhara Misra and Subhas C. Nandya
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.subject Color spanning sets en_US
dc.subject Computational geometry en_US
dc.subject Parameterized complexity en_US
dc.subject Exact algorithms en_US
dc.title Color spanning objects: algorithms and hardness results en_US
dc.type Article en_US
dc.relation.journal Discrete Applied Mathematics

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