Approximating the spanning star forest problem and its applications to genomic sequence alignment

Authors:
C. Thach Nguyen;Jian Shen;Minmei Hou;Li Sheng;Webb Miller;Louxin Zhang
Affiliations:
National University of S'pore, S'pore;Texas State University, San Marcos, TX;The Penn State University, University Park, PA;Drexel University, Philadelphia, PA;The Penn State University, University Park, PA;National University of S'pore, S'pore
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

This paper studies the algorithmic issues of the spanning star forest problem. We prove the following results: (1) there is a polynomial-time approximation scheme for planar unweighted graphs; (2) there is a polynomial-time algorithm with approximation ratio 3/5 for unweighted graphs; (3) it is NP-hard to approximate the problem within ratio 545/546 + ε for unweighted graphs; (4) there is a linear-time algorithm to compute the maximum star forest of a weighted tree; (5) there is a polynomial-time algorithm with approximation ratio 1/2 for weighted graphs. We also show how to apply this spanning star forest model to aligning multiple genomic sequences over a tandem duplication region.