Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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Author: search.filters.author.La, Richard J.Subject: search.filters.subject.approximation algorithms

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    Coloring Rooted Subtrees on a Bounded Degree Host Tree
    (2007) Rawat, Anuj; Shayman, Mark; La, Richard J.; Marcus, Steven I.
    We consider a rooted tree R to be a rooted subtree of a given tree T if the tree obtained by replacing the directed arcs of R by undirected edges is a subtree of T. In this work, we study the problem of assigning colors to a given set of rooted subtrees of a given host tree such that if any two rooted subtrees share a directed edge, then they are assigned different colors. The objective is to minimize the total number of colors used in the coloring. The problem is NP hard even in the case when the degree of the host tree is restricted to 3. This problem is motivated by the problem of assigning wavelengths to multicast traffic requests in all-optical tree networks. We present a greedy coloring scheme for the case when the degree of the host tree is restricted to 3 and prove that it is a 5/2-approximation algorithm. We then present another simpler coloring scheme and prove that it is an approximation algorithm for the problem with approximation ratio 10/3, 3 and 2 for the cases when the degree of the host tree is restricted to 4, 3, and 2, respectively.