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Strings with don't care symbols, also called partial words, and more general indeterminate strings are a natural representation of strings containing uncertain symbols. A considerable effort has been made to obtain efficient algorithms for pattern matching and periodicity detection in such strings. Among those, a number of algorithms have been proposed that behave well on random data, but still their worst-case running time is Theta(n^2). We present the first truly subquadratic-time solutions for a number of such problems on partial words that can also be adapted to indeterminate strings over a constant-sized alphabet. We show that $n$ longest common compatible prefix queries (which correspond to longest common extension queries in regular strings) can be answered on-line in O(n * sqrt(n * log(n)) time after O(n * sqrt(n * log(n))-time preprocessing. We also present O(n * sqrt(n * log(n))-time algorithms for computing the prefix array and two types of border array of a partial word.

Many Combinatorial programming problems are NP-hard (Non Linear Polynomial), and we consider one of them called P path minimum distance connectivity from head quarter to the cities. Let there be n cities and the distance matrix D(i, j, k) is given from ithcity to jthcity using kthfacility. There can be an individual factor which influences the distances/cost and that factor is represented as a facility k. We consider m