Template-Driven Rainbow Coloring of Proper Interval Graphs

Abstract

For efficient design of parallel algorithms on multiprocessor architectures with memory banks, simultaneous access to a specified subgraph of a graph data structure by multiple processors requires that the data items belonging to the subgraph reside in distinct memory banks. Such “conflict-free” access to parallel memory systems and other applied problems motivate the study of rainbow coloring of a graph, in which there is a fixed template T (or a family of templates), and one seeks to color the vertices of an input graph G with as few colors as possible, so that each copy of T in G is rainbow colored, i.e., has no two vertices the same color. In the above example, the data structure is modeled as the host graph G, and the specified subgraph as the template T. We call such coloring a template-driven rainbow coloring (or TR-coloring). For large data sets, it is also important to ensure that no memory bank (color) is overloaded, i.e., the coloring is as balanced as possible. Additionally, for fast access to data, it is desirable to quickly determine the address of a memory bank storing a data item. For arbitrary topology of G and T, finding an optimal and balanced TR-coloring is a challenging problem. This paper focuses on rainbow coloring of proper interval graphs (as hosts) for cycle templates. In particular, we present an O(k· | V| + | E| ) time algorithm to find a TR-coloring of a proper interval graph G with respect to k-length cycle template, Ck. Our algorithm produces a coloring that is (i) optimal, i.e., it uses minimum possible number of colors in any TR-coloring; (ii) balanced, i.e, the vertices are evenly distributed among the different color classes; and (iii) explicit, i.e., the color assigned to a vertex can be computed by a closed form formula in constant time.

Meeting Name

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Department(s)

Computer Science

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Proper interval graph; Rainbow coloring; Template; TRB-coloring

International Standard Book Number (ISBN)

978-303067898-2

International Standard Serial Number (ISSN)

0302-9743; 1611-3349

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2021

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