Giannopoulou, Archontia C. and Mertzios, George B. and Niedermeier, Rolf (2017) 'Polynomial fixed-parameter algorithms : a case study for longest path on interval graphs.', Theoretical computer science., 689 . pp. 67-95.
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path, that is, given an undirected graph, find a maximum-length path in G. Longest Path is NP-hard in general but known to be solvable in O(n4) time on n-vertex interval graphs. We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k9n) time. Notably, Longest Path is trivially solvable in linear time on proper interval graphs, and the parameter value k can be approximated up to a factor of 4 in linear time. From a more general perspective, we believe that using parameterized complexity analysis may enable a refined understanding of efficiency aspects for polynomial-time solvable problems similarly to what classical parameterized complexity analysis does for NP-hard problems.
|Full text:||(AM) Accepted Manuscript|
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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|Publisher Web site:||https://doi.org/10.1016/j.tcs.2017.05.017|
|Publisher statement:||© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/|
|Date accepted:||21 May 2017|
|Date deposited:||05 June 2017|
|Date of first online publication:||25 May 2017|
|Date first made open access:||25 May 2018|
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