## A spectral algorithm for seriation and the consecutive ones problem (1998)

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Venue: | SIAM Journal on Computing |

Citations: | 45 - 0 self |

### BibTeX

@ARTICLE{Atkins98aspectral,

author = {Jonathan E. Atkins and Erik G. Boman and Bruce Hendrickson},

title = {A spectral algorithm for seriation and the consecutive ones problem},

journal = {SIAM Journal on Computing},

year = {1998},

volume = {28},

pages = {297--310}

}

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### Abstract

Abstract. In applications ranging from DNA sequencing through archeological dating to sparse matrix reordering, a recurrent problem is the sequencing of elements in such a way that highly correlated pairs of elements are near each other. That is, given a correlation function f reflecting the desire for each pair of elements to be near each other, find all permutations π with the property that if π(i) < π(j) < π(k) then f(i, j) ≥ f(i, k) and f(j, k) ≥ f(i, k). This seriation problem is a generalization of the well-studied consecutive ones problem. We present a spectral algorithm for this problem that has a number of interesting features. Whereas most previous applications of spectral techniques provide only bounds or heuristics, our result is an algorithm that correctly solves a nontrivial combinatorial problem. In addition, spectral methods are being successfully applied as heuristics to a variety of sequencing problems, and our result helps explain and justify these applications.