Adiga, Abhijin and Babu, Jasine and Chandran, Sunil L (2012) Polynomial time and parameterized approximation algorithms for boxicity. In: Proceedings of 7th International Symposium, IPEC 2012, September 1214, 2012, Ljubljana, Slovenia, pp. 135146.

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Abstract
The boxicity (cubicity) of a graph G, denoted by box(G) (respectively cub(G)), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (cubes) in ℝ k . The problem of computing boxicity (cubicity) is known to be inapproximable in polynomial time even for graph classes like bipartite, cobipartite and split graphs, within an O(n 0.5 − ε ) factor for any ε > 0, unless NP = ZPP. We prove that if a graph G on n vertices has a clique on n − k vertices, then box(G) can be computed in time n22O(k2logk) . Using this fact, various FPT approximation algorithms for boxicity are derived. The parameter used is the vertex (or edge) edit distance of the input graph from certain graph families of bounded boxicity  like interval graphs and planar graphs. Using the same fact, we also derive an O(nloglogn√logn√) factor approximation algorithm for computing boxicity, which, to our knowledge, is the first o(n) factor approximation algorithm for the problem. We also present an FPT approximation algorithm for computing the cubicity of graphs, with vertex cover number as the parameter.
Item Type:  Conference Paper 

Publication:  Parameterized and Exact Computation 
Publisher:  Springer Berlin Heidelberg 
Additional Information:  Copyright of this article belongs to Springer Berlin Heidelberg. 
Keywords:  Boxicity; Parameterized Algorithm; Approximation Algorithm 
Department/Centre:  Division of Electrical Sciences > Computer Science & Automation 
Date Deposited:  04 Nov 2013 09:29 
Last Modified:  04 Nov 2013 09:32 
URI:  http://eprints.iisc.ac.in/id/eprint/47704 
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