The geometry of scheduling

We consider the following general scheduling problem. The input consists of $n$ jobs, each with an arbitrary release time, size, and monotone function specifying the cost incurred when the job is completed at a particular time. The objective is to find a preemptive schedule of minimum aggregate cost. This problem formulation is general enough to include many natural scheduling objectives, such as total weighted flow time, total weighted tardiness, and sum of flow time squared. We give an $O(\log \log P )$ approximation for this problem, where $P$ is the ratio of the maximum to minimum job size. We also give an $O(1)$ approximation in the special case of identical release times. These results are obtained by reducing the scheduling problem to a geometric capacitated set cover problem in two dimensions

The one-dimensional Euclidean domain : finitely many obstructions are not enough

We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature. Keywords: preference representation, spatial elections, group decision makin

The one-dimensional Euclidean domain:finitely many obstructions are not enough

\u3cp\u3eWe show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.\u3c/p\u3

Tight bounds for double coverage against weak adversaries

We study the Double Coverage (DC) algorithm for the k-server problem in the (h, k)-setting, i.e. when DC with k servers is compared against an offline optimum algorithm with h≤k h≤k servers. It is well-known that DC is k-competitive for h=k h=k . We prove that even if k>h k>h the competitive ratio of DC does not improve; in fact, it increases up to h+1 h+1 as k grows. In particular, we show matching upper and lower bounds of k(h+1)k+1 k(h+1)k+1 on the competitive ratio of DC on any tree metric

Fifty years of scheduling: a survey of milestones

Scheduling has become a major field within operational research with several hundred publications appearing each year. This paper explores the historical development of the subject since the mid 1950s when the landmark publications started to appear. A discussion of the main topics of scheduling research for the past five decades is provided, highlighting the key contributions that helped shape the subject. The main topics covered in the respective decades are combinatorial analysis, branch and bound, computational complexity and classification, approximate solution algorithms, and enhanced scheduling models