Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Approximation Algorithms for Minimum-Time Broadcast
SIAM Journal on Discrete Mathematics
Combinatorial logarithmic approximation algorithm for directed telephone broadcast problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Message Multicasting in Heterogeneous Networks
SIAM Journal on Computing
On the inapproximability of broadcasting time
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation Algorithms for Minimum-Time Broadcast under the Vertex-Disjoint Paths Mode
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
The topology aware file distribution problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Information Processing Letters
The topology aware file distribution problem
Journal of Combinatorial Optimization
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Consider a network of processors modeled by an n-vertex graph G=(V,E). Assume that the communication in the network is synchronous, i.e., occurs in discrete ''rounds,'' and in every round every processor is allowed to pick one of its neighbors, and to send it a message. The telephone k-multicast problem requires to compute a schedule with minimal number of rounds that delivers a message from a given single processor, that generates the message, to all the processors of a given set T@?V, |T|=k, whereas the processors of V@?T may be left uninformed. The case T=V is called broadcast problem. Several approximation algorithms with a polylogarithmic ratio were suggested for these problems, and the upper bound on their approximation threshold stands currently on O(logk) and O(logn), respectively. In this paper we devise an O(logkloglogk)-approximation algorithm for the k-multicast problem, and, consequently, an O(lognloglogn)-approximation algorithm for the broadcast problem. Even stronger than that, whenever an instance of the k-multicast problem admits a schedule of length br^*, our algorithm guarantees an approximation ratio of O(logklogbr^*). As br^* is always at least logk, the ratio of O(logkloglogk) follows. In addition, whenever br^*=@W(k^@d) for some constant @d0, we obtain a constantO(1/@d)-approximation ratio for the problem. Our results have implications for network design. The poise of a spanning tree is the sum of its depth and maximum degree [R. Ravi, Rapid rumor ramification: Approximating the minimum broadcast time, in: Proceedings of the IEEE Symposium on Foundations of Computer Science, FOCS '94, 1994, pp. 202-213]. We improve the O(logk) approximation algorithm [A. Bar-Noy, S. Guha, J. Naor, B. Schieber, Multicasting in heterogeneous networks, SIAM J. Comput. 30 (2) (2000) 347-358] for the poise problem to O(logk/logklogk), and obtain an improved (O(logk/loglogk),O(logk/logklogk)) bicriteria approximation for the depth-degree problem. We also derive results concerning the edge-dependent heterogeneous k-multicast problem.