Computing input multiplicity in anonymous synchronous networks with dynamic faults

Abstract

We consider the following problem: Each processor of the network has assigned a (not necessarily unique) input value. Determine the 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 an anonymous synchronous network of arbitrary topology, in which dynamic link faults [P. Fraigniaud, C. Peyrat, Inform. Process. Lett. 71 (1999) 115-119; N. Santoro, P. Widmayer, in: Proc. SIGAL'90, Tokyo, 1990, in: LNCS, Springer, Berlin, 1990, pp. 358-369] may occur. An instance of this problem has been stated as an open problem by N. Santoro at the rump session of 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. © 2004 Elsevier B.V. All rights reserved.