Resource Allocation in Bounded Degree Trees

Reuven Bar-Yehuda, Michael Beder, Yuval Cohen, Dror Rawitz

Research output: Contribution to journalArticlepeer-review


We study the bandwidth allocation problem (bap) in bounded degree trees. In this problem we are given a tree and a set of connection requests. Each request consists of a path in the tree, a bandwidth requirement, and a weight. Our goal is to find a maximum weight subset S of requests such that, for every edge e, the total bandwidth of requests in S whose path contains e is at most 1. We also consider the storage allocation problem (sap), in which it is also required that every request in the solution is given the same contiguous portion of the resource in every edge in its path. We present a deterministic approximation algorithm for bap in bounded degree trees with ratio (2√e-1)/( √e-1)+ ε <3.542 . Our algorithm is based on a novel application of the local ratio technique in which the available bandwidth is divided into narrow strips and requests with very small bandwidths are allocated in these strips. We also present a randomized (2+ε)-approximation algorithm for bap in bounded degree trees. The best previously known ratio for bap in general trees is 5. We present a reduction from sap to bap that works for instances where the tree is a line and the bandwidths are very small. It follows that there exists a deterministic 2.582-approximation algorithm and a randomized (2+ε)-approximation algorithm for sap in the line. The best previously known ratio for this problem is 7.

Original languageEnglish
Pages (from-to)89-106
Number of pages18
Issue number1
StatePublished - May 2009
Externally publishedYes


  • Approximation algorithms
  • Bandwidth allocation
  • Bounded degree trees
  • Scheduling
  • Storage allocation


Dive into the research topics of 'Resource Allocation in Bounded Degree Trees'. Together they form a unique fingerprint.

Cite this