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 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 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.