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> ≥ 1, a positive weight, <i>w<inf>j</inf>,</i> and two jobs are in conflict if any of… (More)
The concept of submodularity plays a vital role in com-binatorial optimization. In particular, many important optimization problems can be cast as submodu-lar maximization problems, including maximum coverage , maximum facility location and max cut in di-rected/undirected graphs. In this paper we present the first known approximation algorithms for the… (More)
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)
For a video-on-demand computer system we propose a scheme which balances the load on the disks, thereby helping to solve a performance problem crucial to achieving maximal video throughput. Our load balancing scheme consists of two components. The static component determines good assignments of videos to groups of striped disks. The dynamic component uses… (More)
We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of diierent classes (colors) need to be placed in bins; the items may have diierent sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can hold. In the class-constrained multiple knapsack (CCMK)… (More)
Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider <i>information spreading</i> among <i>n</i> nodes of a network, where each node <i>v</i> has a message <i>m(v)</i> which must be received by all other nodes. The time required for information spreading has been… (More)
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)
Let M = (E, I) be a matroid, and let S be a family of subsets of size p of E.