We consider the problem of scheduling jobs that are given as <i>groups</i> of non-intersecting segments on the real line. Each job <i>J<inf>j</inf></i> is associated with an interval, <i>I<inf>j</inf>,</i> which consists of up to <i>t</i> segments, for some <i>t</i> &#8805; 1, a positive weight, <i>w<inf>j</inf>,</i> and two jobs are in conflict if any of(More)
• SODA
• 2009
The concept of submodularity plays a vital role in combinatorial optimization. In particular, many important optimization problems can be cast as submodular maximization problems, including maximum coverage, maximum facility location and max cut in directed/undirected graphs. In this paper we present the first known approximation algorithms for the problem(More)
We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = &#x007B;J<inf>1</inf>, &#x2026; , J<inf>n</inf>&#x007D;. Each job, J<inf>j</inf>, is associated with an interval [s<inf>j</inf>, c<inf>j</inf>] along which it should be processed. Also given is the(More)
• FSTTCS
• 2010
<lb>We consider the following fundamental scheduling problem. The input consists of n jobs to be sched-<lb>uled on a set of machines of bounded capacities. Each job is associated with a release time, a due<lb>date, a processing time and demand for machine capacity. The goal is to schedule all of the jobs<lb>non-preemptively in their release-time-deadline(More)
• Algorithmica
• 2001
We study two variants of the classic knapsack problem, in which we need to place items of <e5>different types</e5> in multiple knapsacks; each knapsack has a limited capacity, and a bound on the number of different types of items it can hold: in the <e5>class-constrained multiple knapsack problem (CMKP)</e5> we wish to maximize the total number of packed(More)
• 7
• ACM Trans. Algorithms
• 2004
The <i>data migration</i> problem is to compute an efficient plan for moving data stored on devices in a network from one configuration to another. We consider this problem with the objective of minimizing the sum of completion times of all storage devices. It is modeled by a transfer graph, where vertices represent the storage devices, and the edges(More)
• ACM Trans. Algorithms
• 2002
We consider the following scheduling with batching problem that has many applications, e.g., in multimedia-on-demand and manufacturing of integrated circuits. The input to the problem consists of <i>n</i> jobs and <i>k</i> parallel machines. Each job is associated with a set of time intervals in which it can be scheduled (given either explicitly or(More)