@inproceedings{28f244d27dca47628805fa7a79ed991a,

title = "All-norm approximation algorithms",

abstract = "A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different l p norms. We address this problem by introducing the concept of an All-norm ¿-approximation algorithm, which supplies one solution that guarantees ¿-approximation to all l p norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [12] showed a 2-approximation algorithm for the problem with respect to the l8 norm. For any fixed l p norm the previously known approximation algorithm has a performance of ¿(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given l p norm (p > 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given l p norm a FPTAS for any fixed number of machines.",

author = "Y. Azar and L. Epstein and Y. Richter and G.J. Woeginger",

year = "2002",

doi = "10.1007/3-540-45471-3_30",

language = "English",

isbn = "3-540-43866-1",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "288--297",

editor = "M. Penttonen and E.M. Schmidt",

booktitle = "Algorithm Theory - SWAT 2002 (Proceedings of the 8th Scandinavian Workshop on Algorithm Theory, Turku, Finland, July 3-5, 2002)",

address = "Germany",

}