A new method for solving the hitting set problem is proposed. This method is based on the mapping of the problem onto an integer programming optimization problem. This new approach provides an algorithm with much better performance compare to the algorithms for the bitting set problem that currently are used for solving the diagnosis problem. The relation of this approach with the satisfiabilit...

Continuous Conceptual Set Covering (CCSC) is an algorithm that uses engineering knowledge to learn operator effects from training examples. The program produces an operator hypothesis that, even in noisy and nondeterministic domains, can make good quantitative predictions. An empirical evaluation in the traytilting domain shows that CCSC learns faster than an alternative case-based approach. Th...

In this paper we present a novel extended formulation for the line planning problem that is based on what we call “configurations” of lines and frequencies. Configurations account for all possible options to provide a required transportation capacity on an infrastructure edge. The proposed configuration model is strong in the sense that it implies several facet-defining inequalities for the sta...

Marchand and Shawe-Taylor (2002) have proposed a loss bound for the set covering machine that has the property to depend on the observed fraction of positive examples and on what the classifier achieves on the positive training examples. We show that this loss bound is incorrect. We then propose a loss bound, valid for any sample-compression learning algorithm (including the set covering machin...

Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual assessments, they may not always be consistent. The level of inconsistency among individual assessments is widely accepted as a measure of the ranking quality...

In this report, we will introduce an optimization problem called Maximum Density Set Cover Problem. We firstly prove it is a NP-hard problem and then we analyse its approximation algorithms. The performance guarantee of one of the approximation algorithms is θ( √ n). Experiment is conducted to verify the algorithms’ performance.

We revisit the traveling salesman problem with neighborhoods (TSPN) and present the first constant-ratio approximation for disks in the plane: Given a set of n disks in the plane, a TSP tour whose length is at most O(1) times the optimal can be computed in time that is polynomial in n. Our result is the first constant-ratio approximation for a class of planar convex bodies of arbitrary size and...

In this paper, we consider the generalized min-sum set cover problem, introduced by Azar, Gamzu, and Yin [1]. Bansal, Gupta, and Krishnaswamy [2] give a 485approximation algorithm for the problem. We are able to alter their algorithm and analysis to obtain a 28-approximation algorithm, improving the performance guarantee by an order of magnitude. We use concepts from α-point scheduling to obtai...

Several researchers have employed the notion of reliability of coverage to extend the set covering and maximal coverage models. We discuss the suitability of such reliability models in general for choosing ambulance station or vehicle locations. Then, we discuss one representative model from this class of models (the queueing maximum availability location problem) in greater detail and describe...