• Discrete Applied Mathematics
• 2004
The bin-packing problem asks for a packing of a list of items of sizes from (0; 1] into the smallest possible number of bins having unit capacity. The k-item bin-packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two e6cient on-line algorithms for this problem. We show that, for increasing values ofâ€¦ (More)
• Oper. Res. Lett.
• 2013
A sequence of items that can be packed into m bins of unit size has to be assigned online to the bins minimizing the stretching factor, i.e., to stretch the bin sizes as little as possible such that the items fit into the bins. We present an elementary algorithmwith stretching factor 11/7 improving the best known algorithm by Cheng et al. (2005) [5] with aâ€¦ (More)
• 5
• Theor. Comput. Sci.
• 2005
We are given a set of identical machines and a sequence of jobs, the sum of whose weights is known in advance. The jobs are to be assigned on-line to one of the machines and the objective is to minimize the makespan. An algorithm with performance ratio 1.6 and a lower bound of 1.5 is presented. These results improve on the recent results by Azar and Regev,â€¦ (More)
• MichaÃ«l Gabaya
• 2013
We are given a sequence of items that can be packed into m unit size bins and the goal is to assign these items online tom bins while minimizing the stretching factor. Bins have in nite capacities and the stretching factor is the size of the largest bin. We present an algorithm with stretching factor 26/17 improving the best known algorithm by Kellerer andâ€¦ (More)
• J. Scheduling
• 2008
In this paper we consider the problem of scheduling n jobs on a single machine, where the jobs are processed in batches and the processing time of each job is a step function depending on its waiting time, which is the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. For job i, if itsâ€¦ (More)
• Inf. Process. Lett.
• 2006
We consider the online scheduling problem with m âˆ’ 1, m â‰¥ 2, uniform machines each with a processing speed of 1, and one machine with a speed of s, 1 â‰¤ s â‰¤ 2, to minimize the makespan. The wellknown list scheduling (LS) algorithm has a worst-case bound of 3mâˆ’1 m+1 [1]. An algorithm with a better competitive ratio was proposed in [3]. It has a worst-caseâ€¦ (More)