This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains greatest number of uncovered elements and adds the selected p sets to partial set cover. The process of adding p sets is repeated until all the elements are covered...

The Set Covering Machine (SCM) was introduced by Marchand & Shawe–Taylor [6, 7] in which a minimum set cover of a class of examples was approximated to find a compact conjunction/disjunction of features for classification. Their approach was to solve the set cover problem using the greedy algorithm. In this paper we introduce an alternative method of solving the SCM by formulating it as a Linea...

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...

The Set Covering Machine (SCM) is a machine learning algorithm that constructs a conjunction of Boolean functions. This algorithm is motivated by the minimization of a theoretical bound. However, finding the optimal conjunction according to this bound is a combinatorial problem. The SCM approximates the solution using a greedy approach. Even though SCM seems very efficient in practice, it is un...

Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusionexclusion ...

In this paper, we consider two new variants of the unit covering problem in color-spanning set model: Given a set of n points in d-dimensional plane colored with m colors, the MinCSBC problem is to select m points of different colors minimizing the minimum number of unit balls needed to cover them. Similarly, the MaxCSBC problem is to choose one point of each color to maximize the minimum numbe...

We consider multilevel set-covering models for diagnostic reasoning: though a lot of work has been done in this field, knowledge acquisition efforts have been investigated only insufficiently. We will show how set-covering models can be build incrementally and how they can be refined by knowledge enhancements or representational extensions. All these extensions have a primary characteristic: th...

This paper describes new set covering algorithms associated with the DISCRETE edit system. DISCRETE is based on the Fellegi-Holt model (JASA 1976) of editing. A new implicit-edit generation algorithm replaces algorithms of Garfinkel, Kunnathur, and Liepins (Operations Research 1986) and Winkler (1995). The new set-covering algorithms correctly generate implicit edits for large subclasses and re...

In this case study we consider the set covering problem, the classical operations research problem of covering the rows of a zero-one matrix by a subset of the columns at minimum cost. We outline a genetic-algorithm-based heuristic for the problem. The key features of this genetic algorithm are a binary representation, drawn naturally from a zero-one formulation of the problem, a new crossover ...

not submitted. Designing and building synthetic signal transduction circuitry in yeast Stephen Checkley Manchester The yeast Saccharomyces cerevisiae possesses an intracellular signal transduction pathway enabling this organism to initiate a developmental response upon detection of a peptide mating pheromone. This developmental response is the focus of this study. The project aims to modify the...