Abstract
We consider the following problem: Each processor of the network has assigned a (not necessarily unique) input value. Determine multiplicity of each input value. Solving this problem means any input-symmetric function (i.e. function not sensitive to permutations of its input values) can be computed. We consider anonymous synchronous networks of arbitrary topology, in which dynamic link faults [3,6] may occur.
An instance of this problem has been stated as an open problem by N. Santoro at SIROCCO’98: Is it possible to distributively compute parity function (XOR) on anonymous hypercubes with dynamic faults?
We show that if the network size N (the number of processors) is known, the multiplicity of inputs (and thus any input-symmetric function) can be computed on any connected network. The time complexity depends on the details of the model and the amount of topological information, but it is always a low polynomial in N.
Supported by VEGA grant No. 2/7007/20.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chlebus, B. S.-Diks, K.-Pelc, A.: Broadcasting in Synchronous Networks with Dynamic Faults, Networks, 27 (1996), pp. 309–318.
Dobrev, S.-Vrto, I.: Optimal broadcasting in hypercubeswith dynamic faults, Information Processing Letters 71 (1999), pp 81–85.
Fraigniaud, P.-Peyrat, C.: Broadcasting in a hypercube when some calls fail, Information Processing Letters 39 (1991), pp. 115–119.
De Marco, G.-Vaccaro, U.: Broadcasting in hypercubes and star graphs with dynamic faults, Information Processing Letters 66 (1998). pp. 321–326.
Pelc, A,: Fault-tolerant broadcasting and gossiping in communication networks, Networks 28 (1996), pp. 143–156.
Santoro, N.-Widmayer, P.: Distributed function evaluation in presence of transmission faults, in Proc. of SIGAL’90, Tokyo, 1990; LNCS 450, Springer Verlag, 1990, pp. 358–369.
Yamashita, M.-Kameda, T. Computing on an anonymous networks, in Proc. of PODC’88, 1988, pp. 117–130.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dobrev, S. (2000). Computing Input Multiplicity in Anonymous Synchronous Networks with Dynamic Faults. In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_14
Download citation
DOI: https://doi.org/10.1007/3-540-40064-8_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41183-3
Online ISBN: 978-3-540-40064-6
eBook Packages: Springer Book Archive