Approximation algorithms for partially colorable graphs

Ghoshal, S and Louis, A and Raychaudhury, R (2019) Approximation algorithms for partially colorable graphs. In: 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019, 20 - 22 September 2019, Cambridge.

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Abstract

Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For α ≤ 1 and k ∈ Z+, we say that a graph G = (V, E) is α-partially k-colorable, if there exists a subset S ⊂ V of cardinality |S| ≥ α|V | such that the graph induced on S is k-colorable. Partial k-colorability is a more robust structural property of a graph than k-colorability. For graphs that arise in practice, partial k-colorability might be a better notion to use than k-colorability, since data arising in practice often contains various forms of noise. We give a polynomial time algorithm that takes as input a (1 − ∊)-partially 3-colorable graph G and a constant γ ∈ [∊, 1/10], and colors a (1 − ∊/γ) fraction of the vertices using Õ (Formula presented.) colors. We also study natural semi-random families of instances of partially 3-colorable graphs and partially 2-colorable graphs, and give stronger bi-criteria approximation guarantees for these family of instances.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Keywords:	Approximation algorithms; Combinatorial optimization; Computation theory; Graphic methods; Polynomial approximation; Random processes, Bi-criteria; Cardinalities; Colorability; Graph coloring problem; Polynomial-time algorithms; Semi-random; Semi-random models; Vertex coloring, Graph theory
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	07 Jan 2023 05:01
Last Modified:	07 Jan 2023 05:01
URI:	https://eprints.iisc.ac.in/id/eprint/78845

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