Bound smoothing under chirality constraints
SIAM Journal on Discrete Mathematics
A robust model for finding optimal evolutionary trees
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient algorithms for inverting evolution
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
On constructing radiation hybrid maps (extended abstract)
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Building human genome maps with radiation hybrids
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Placing Probes along the Genome Using Pairwise Distance Data
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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The MATRIX-TO-LINE problem is that of, given an n × n symmetric matrix D, finding an arrangement of n points on the real line such that the so obtained distances agree as well as possible with the by D specified distances, w.r.t. the max-norm. The MATRIX-TO-LINE problem has previously been shown to be NP-complete [11]. We show that it can be approximated within 2, but not within 4=3 unless P=NP. We also show tight bounds under a stronger assumption. We show that the MATRIX-TO-LINE problem cannot be approximated within 2 - δ unless 3-colorable graphs can be colored with ⌊4/δ⌋ colors in polynomial time. Currently, the best polynomial time algorithm colors a 3-colorable graph with Õ(n3/14) colors [4]. We apply our MATRIX-TO-LINE algorithm to a problem in computational biology, namely, the Radiation Hybrid (RH) problem, i.e., the algorithmic part of a physical mapping method called RH mapping. This gives us the first algorithm with a guaranteed convergence for the general RH problem.