Copyright © (2004) by IEEE. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distrubuted for profit. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.
We consider a network design problem, where applications require various levels of Quality-of-Service (QoS) while connections have limited performance. Suppose that a source needs to send a message to a heterogeneous set of receivers. The objective is to design a low cost multicast tree from the source that would provide the QoS levels (e.g., bandwidth) requested by the receivers. We assume that the QoS level required on a link is the maximum among the QoS levels of the receivers that are connected to the source through the link. In accordance, we define the cost of a link to be a function of the QoS level that it provides. This definition of cost makes this optimization problem more general than the classical Steiner tree problem. We consider several variants of this problem all of which are proved to be NP-Hard. For the variant where QoS levels of a link can vary arbitrarily and the cost function is linear in its QoS level, we give a heuristic that achieves a multicast tree with cost at most a constant times the cost of an optimal multicast tree. The constant depends on the best constant approximation ratio of the classical Steiner tree problem. For the more general variant, where each link has a given QoS level and cost we present a heuristic that generates a multicast tree with cost O(min{log r; k}) times the cost of an optimal tree, where r denotes the number of receivers, and k denotes the number of different levels of QoS required. We generalize this result to hold for the case of many multicast groups.
By: Moses Charikar, Joseph Naor, Baruch Schieber
Published in: IEEE/ACM Transactions on Networking, volume 12, (no 2), pages 340-8 in 2004
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .