Abstract
Co-path Set problem is of important applications in mapping unique DNA sequences onto chromosomes and whole genomes. Given a graph G, the parameterized version of Co-path Set problem is to find a subset F of edges with size at most k such that each connected component in \(G[E\backslash F]\) is a path. In this paper, we give a kernel of size 6k and a randomized algorithm of running time \(O^*(2.17^k)\) for the Parameterized Co-path Set problem. The randomized methods developed in the paper are of great promising to be applied to other branch-based algorithms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cox DR, Burmeister M, Price ER, Kim S, Myers RM (1990) Radiation hybrid mapping: a somatic cell genetic method for constructing high resolution maps of mammalian chromosomes. Science 250:245–250
Cheng Y, Cai Z, Goebel R, Lin G, Zhu B (2008) The radiation hybrid map construction problem: recognition, hardness, and approximation algorithms. Unpublished Manuscript
Chen J, Feng Q (2014) On unknown small subsets and implicit measures: new techniques for parameterized algorithms. J Comput Sci Technol 29(5):870–878
Chen Z, Lin G, Wang L (2011) An approximation algorithm for the minimum co-path set problem. Algorithmica 60(4):969–986
Feng Q, Wang J, Li S, Chen J (2015) Randomized parameterized algorithms for P\(_2\)-Packing and Co-Path Packing problems. J Comb Optim 29(1):125–140
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP completeness. W. H. Freeman, New York
Heggernes P, Hof P, Lvque B, Lokshtanov D, Paul C (2014) Contracting graphs to paths and trees. Algorithmica 68(1):109–132
Jiang H, Zhang C, Zhu B (2010) Weak kernels. ECCC Report, TR10-005, 2010
Richard CW, Withers DA, Meeker TC, Maurer S, Evans GA, Myers RM, Cox DR (1991) A radiation hybrid map of the proximal long arm of human chromosome 11, containing the multiple endocrine neoplasia type 1 (MEN-1) and bcl-1 disease loci. Am J Hum Genet 49:1189–1196
Slonim D, Kruglyak L, Stein L, Lander E (1997) Building human genome maps with radiation hybrids. J Comput Biol 4:487–504
Zhang C, Jiang H, Zhu B (2012) Radiation hybrid map construction problem parameterized. Proceedings of 6th international conference on combinatorial optimization and applications (COCOA 2012). Lecture Notes in Computer Science, vol. 7402. Springer, Berlin, pp. 127–137
Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grant (61232001, 61472449, 61420106009), the Research Fund for the Doctoral Program of Higher Education of China (NO.20130162130001) and the Major Science & Technology Research Program for Strategic Emerging Industry of Hunan (Grant No. 2012GK4054).
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this work was reported in the Proceedings of the 8th International Frontiers of Algorithmics Workshop, Lecture Notes in Computer Science, vol. 8497, 2014, pp. 82–93.
Rights and permissions
About this article
Cite this article
Feng, Q., Zhou, Q. & Wang, J. Kernelization and randomized Parameterized algorithms for Co-path Set problem. J Comb Optim 32, 67–78 (2016). https://doi.org/10.1007/s10878-015-9901-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-015-9901-y