Strictly Chordality-k graphs (SCk) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For k ≥ 5, the study has been recently initiated in [1] and various structural and algorithmic results are reported. In this paper, we show that ma...

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family P is affinely reduced to a family Q if for every pol...

A key challenge in cancer genomics is the identification and prioritization of genomic aberrations that potentially act as drivers of cancer. In this paper we introduce HIT’nDRIVE, a combinatorial method to identify aberrant genes that can collectively influence possibly distant “outlier” genes based on what we call the “random-walk facility location” (RWFL) problem on an interaction network. R...

We study in this article polynomial approximation of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the frequency of each element is bounded by a constant)...

Many learning systems implicitly use the fit-andsplit learning method to create a comprehensive hypothesis from a set of partial hypotheses. At the core of the fit-and-split method is the assignment of examples to partial hypotheses. To date, however, this core has been neglected. This paper provides the first definition and model of the fit-and-split assignment problem. Extant systems perform ...

We study the complexity of several parameterizations for max k-set cover. Given a family of subsets S = {S1, . . . , Sm} over a set of elements X = {x1, . . . , xn} and an integer p, max k-set cover consists of finding a set T of at most k subsets covering at least p elements. This problem, when parameterized by k, is W[2]-hard. Here, we settle the multiparameterized complexity of max k-set cov...

We define a NP-hard clustered variant of the Set Covering Problem where subsets are partitioned into K clusters and a fixed cost is paid for selecting at least one subset in a given cluster. This variant can reformulate as a master problem various multi-commodity flow problems in transportation planning. We show that the problem is approximable within ratio (1+2)(e/e−1)H(q), where q is the maxi...