We present a family of approximation algorithms for minimum subset sum with a worst-case approximation ratio of (k + 1)/k and which run in linear time assuming that k is constant. We also present a family of linear-time approximation algorithms for subset sum with worst-case approximation factors of k/(k+1) assuming that k is constant. The algorithms use approaches from and improve upon previou...

Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defi...

Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer m for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In...

This paper describes a multi-spectral, multisource approach to the important problem of speaker identification. The wideband speech signal is filtered into several sub-bands and the output time trajectory of each is individually modeled by linear prediction cepstral coefficients. These individual models are then matched against reference data and the scores combined using the sum rule of inform...

With any (not necessarily proper) edge k-colouring γ : E(G) −→ {1, . . . , k} of a graph G, one can associate a vertex colouring σγ given by σγ(v) = ∑ e∋v γ(e). A neighbour-sumdistinguishing edge k-colouring is an edge colouring whose associated vertex colouring is proper. The neighbour-sum-distinguishing index of a graph G is then the smallest k for which G admits a neighbour-sum-distinguishin...