A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are now consistent with the existing results on connected dominating set problem which is a special case of the minimum connected set cover problem.

K e y w o r d s S e t c o v e r i n g problems, Fuzzy sets, Fuzzy set-covering problem, Algebraic sum operator. 1. I N T R O D U C T I O N A classical set-covering problem considers the subsets I = {1, 2 , . . . , m} and J = {1, 2 , . . . , n} of integers. A collection p of subset Pj of I is a cover of I, if the union of the members of go is I, i.e., let Pj C I, go = {Pj : j C J0}, J0 C J, go i...

Given a collection C of weighted subsets of a ground set E , the set cover problem is to find a minimum weight subset of C which covers all elements of E . We study a strategic game defined upon this classical optimization problem. Every element of E is a player which chooses one set of C where it appears. Following a public tax function, every player is charged a fraction of the weight of the ...

We develop for set cover games several general cost-sharing methods that are approximately budget-balanced, in the core, and/or group-strategyproof. We first study the cost sharing for a single set cover game, which does not have a budgetbalanced mechanism in the core. We show that there is no cost allocation method that can always recover more than 1 ln n of the total cost and in the core. Her...

We analyse a newspaper market where media …rms compete for advertising as well as for readership. Firms …rst choose the political position of their newspaper, then set cover prices and advertising tari¤s. We build on the duopoly work in two-sided markets of Gabszewicz, Laussel, and Sonnac (2001, 2002) who show that advertising …nancing can lead to minimum political di¤erentiation. We extend the...

In this paper we study the set cover games when the elements are selfish agents, each of which has a privately known valuation of receiving the service from the sets, i.e., being covered by some set. Each set is assumed to have a fixed cost. We develop several approximately efficient strategyproof mechanisms that decide, after soliciting the declared bids by all elements, which elements will be...

An unsatisfiable set is a set of formulas whose conjunction is unsatisfiable. Every unsatisfiable set can be corrected, i.e., made satisfiable, by removing a subset of its members. The subset whose removal yields satisfiability is called a correction subset. Given an unsatisfiable set F there is a well known hitting set duality between the unsatisfiable subsets of F and the correction subsets o...

Min Sum Set Cover and its Generalizations Name: Sungjin Im Affil./Addr. Electrical Engineering and Computer Science, University of California, Merced, CA, USA

In this paper we study the set cover games when the elements are selfish agents. In this case, each element has a privately known valuation of receiving the service from the sets, i.e., being covered by some set. Each set is assumed to have a fixed cost. We develop several approximately efficient strategyproof mechanisms, each of which decides, after soliciting the declared bids by all elements...

We analyse a newspaper market where two editors compete for advertising as well as for readership. They first choose the political position of their newspaper, then set cover prices and advertising tariffs. We build on the work of Gabszewicz, Laussel and Sonnac (2001, 2002), whose model we take as the stage game of an infinitely repeated game, and investigate the incentives to collude and the p...