Broadcast networks of bounded degree
SIAM Journal on Discrete Mathematics
Broadcasting in bounded degree graphs
SIAM Journal on Discrete Mathematics
Minimum broadcast time is NP-complete for 3-regular planar graphs and deadline 2
Information Processing Letters
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Multicasting in heterogeneous networks
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The complexity of broadcasting in planar and decomposable graphs
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Bicriteria Network Design Problems
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Approximation Algorithms for Minimum-Time Broadcast under the Vertex-Disjoint Paths Mode
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Sublogarithmic approximation for telephone multicast
Journal of Computer and System Sciences
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We investigate the problem of broadcasting information in a given undirected network. At the beginning information is given at some processors, called sources. Within each time unit step every informed processor can inform only one neighboring processor. The broadcasting problem is to determine the length of the shortest broadcasting schedule for a network, called the broadcasting time of the network. We show that there is no efficient approximation algorithm for the broadcasting time of a network with a single source unless P = NP. More formally, it is NP-hard to distinguish between graphs G = (V,E) with broadcasting time smaller than b ∈ Θ(√|V|) and larger than (57/56 - ∈)b for any ∈ ≥ 0. For ternary graphs it is NP-hard to decide whether the broadcasting time is b ∈ Θ(log |V|) or b + Θ(√b) in the case of multiples sources. For ternary networks with single sources, it is NP-hard to distinguish between graphs with broadcasting time smaller than b ∈ Θ(√|V|) and larger than b + c√log b. We prove these statements by polynomial time reductions from E3-SAT.