Greedy algorithms for on-line set-covering and related problems
Ausiello, Giorgio; Giannakos, Aristotelis; Paschos, Vangelis (2006), Greedy algorithms for on-line set-covering and related problems, in Jay, Barry; Gudmunsson, Joachim, Theory of Computing 2006. Twelfth Computing: The Australasian Theory Symposium (CATS2006), Hobart, Australia, 16-19 January 2006, Australian Computer Society, p. 145-151
TypeCommunication / Conférence
Conference titleTwelfth Computing: The Australasian Theory Symposium (CATS'06)
Book titleTheory of Computing 2006. Twelfth Computing: The Australasian Theory Symposium (CATS2006), Hobart, Australia, 16-19 January 2006
Book authorJay, Barry; Gudmunsson, Joachim
Number of pages154
MetadataShow full item record
Abstract (EN)We study the following on-line model for set-covering: elements of a ground set of size n arrive one-by-one and with any such element ci, arrives also the name of some set Si0 containing ci and covering the most of the uncovered ground set-elements (obviously, these elements have not been yet revealed). For this model we analyze a simple greedy algorithm consisting of taking Si0 into the cover, only if ci is not already covered. We prove that the competitive ratio of this algorithm is pn and that it is asymptotically optimal for the model dealt, since no on-line algorithm can do better than pn=2. We next show that this model can also be used for solving minimum dominating set with competitive ratio bounded above by the square root of the size of the input graph. We finally deal with the maximum budget saving problem. Here, an initial budget is allotted that is destined to cover the cost of an algorithm for solving set-covering. The objective is to maximize the savings on the initial budget. We show that when this budget is at least equal to pn times the size of the optimal (off-line) solution of the instance under consideration, then the natural greedy off-line algorithm is asymptotically optimal.
Subjects / KeywordsBudget saving; Dominating set; Competitive ratio; On-line algorithm; Set-covering
Showing items related by title and author.