PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A lower bound for radio broadcast
Journal of Computer and System Sciences
Approximation Algorithms for Minimum-Time Broadcast
SIAM Journal on Discrete Mathematics
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Multicasting in heterogeneous networks
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On the Hardness of Approximation Spanners
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Sublogarithmic approximation for telephone multicast: path out of jungle (extended abstract)
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing broadcast latency and redundancy in ad hoc networks
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
A note on line broadcast in digraphs under the edge-disjoint paths mode
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
Efficient trigger-broadcasting in heterogeneous clusters
Journal of Parallel and Distributed Computing
Broadcasting on networks of workstations
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Sublogarithmic approximation for telephone multicast
Journal of Computer and System Sciences
Approximation and heuristic algorithms for minimum-delay application-layer multicast trees
IEEE/ACM Transactions on Networking (TON)
Broadcasting in necklace graphs
C3S2E '09 Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering
Approximation algorithm for directed telephone multicast problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Minimum multicast time problem in wireless sensor networks
WASA'06 Proceedings of the First international conference on Wireless Algorithms, Systems, and Applications
Linear algorithm for broadcasting in unicyclic graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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(MATH) Consider a synchronous network of processors, modeled by directed or undirected graph G = (V,E), in which on each round every processor is allowed to choose one of its neighbors and to send him a message. Given a processor s &egr; V, and a subset T ⊆ V of processors, the telephone multicast problem requires to compute the shortest schedule (in terms of the number of rounds) that delivers a message from s to all the processors of T. The particular case T = V is called telephone broadcast problem.These problems have multiple applications in distributed computing. Several approximation algorithms with polylogarithmic ratio, including one with logarithmic ratio, for the undirected variants of these problems are known. However, all these algorithms involve solving large linear programs. Devising a polylogarithmic approximation algorithm for the directed variants of these problems is anopen problem, posed in [15].We devise a combinatorial logarithmic approximation algorithm for these problems, that applies also for the directed broadcast problem. Our algorithm has significantly smaller running time, and seems to reveal more information about the combinatorial structure of the solution, than the previous algorithms, that are based on linear programming.(MATH) We also improve the lower bounds on the approximation threshold of these problems. Both problems are known to be 3/2-inapproximable. For the undirected (resp., directed) broadcast problem we show that it is NP-hard (resp., impossible unless $NP ⊇ DTIME(nO(log n))) to approximate it within a ratio of 3 —&egr; for any &egr; ρ 0 (resp., ω(\sqrt log n)).Finally, we study the radio broadcast problem. Its setting is similar to the telephone broadcast problem, but in every round every processor may either send a message to all its neighbors or may not send it at all. A processor is informed in a certain round if and only if it receives a message from precisely one neighbor.(MATH) This problem was known to admit O(log2 n)-approximation algorithm, but no hardness of approximation was known. In this paper we show that the problem is ω(log n)-inapproximable unless NP ⊆ BPTIME(nlog log n}).