We discuss a simple model for tumor growth, which results in realistic tumor shapes. We then address the question of efficient irradiation of tumors in terms of packing their volume with disjoint spheres of given radii. We develop three algorithms, based on a shelling method, which give recommendations for optimal sphere packings. These packings are interpreted as treatment plans, and the corre...

In this paper we describe an algorithm to approximately solve a class of semidefinite programs called covering semidefinite programs. This class includes many semidefinite programs that arise in the context of developing algorithms for important optimization problems such as Undirected SPARSEST CUT, wireless multicasting, and pattern classification. We give algorithms for covering SDPs whose de...

The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the "HARMONIC" algorithms Hk introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (1985), pp. 562-572 ]. The algorithms in this paper guarantee the worst case performance of Hk, whereas they only use O(log log k) instead ofk active bins. For k >_6, the algorithms in this paper outpe...

We show algorithms for computing representative families matroid intersections and use them in fixed-parameter set packing, covering, facility location problems with multiple constraints. complement our tractability results by hardness results.

In this paper we present a study of the performance of a general class of channel assignment algorithms. These algorithms, which we call R-algorithms, are completely characterized by the set of carried-traffic “states” which they allow. We shall see that for any such algorithm, there is a closed-form expression for the carried t r a c function, which lends itself to several kinds of asymptotic ...

By prior work, there is a distributed graph algorithm that finds a maximal fractional matching (maximal edge packing) in O(∆) rounds, independently of n; here ∆ is the maximum degree of the graph and n is the number of nodes in the graph. We show that this is optimal: there is no distributed algorithm that finds a maximal fractional matching in o(∆) rounds, independently of n. Our work gives th...

Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT Gang scheduling has been widely used as a practical solution to the dynamic parallel job scheduling problem. To overcome some of the limitations of traditional Gang scheduling algorithms, Concurrent Gang is proposed as a class of scheduling policies which allows the exible and simultaneous scheduling of multi...

The P2-packing problem asks whether a graph contains k vertex-disjoint (not necessarily induced) paths each of length two. We continue the study its kernelization algorithms, and develop 5k-vertex kernel.

In this paper we give a short survey on eecient algorithms for Steiner trees and paths packing problems in planar graphs. We particularly concentrate on recent results. The rst result is a linear-time algorithm for packing vertex-disjoint trees resp. paths within a planar graph, where the vertices to be connected lie on at most two diierent faces 26, 32]. This algorithm is based on a linear-tim...

Packing and covering linear programs belong to the narrow class of linear programs that are efficiently solvable in parallel and distributed models of computation, yet are a powerful modeling tool for a wide range of fundamental problems in theoretical computer science, operations research, and many other areas. Following recent progress in obtaining faster distributed and parallel algorithms f...