This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions. The proofs are achi...

In this research, we present an improved version of Bidirectional (BD) exact pattern matching (EPM) algorithm to solve the problem of exact pattern matching. Improved-Bidirectional (IBD) exact pattern matching algorithm introduced a new idea of scanning partial text window (PTW) as well with the pattern to take decision of moving pattern to the right of partial text window. IBD algorithm compar...

We consider the problem of finding an instance of a string-pattern s in a given string under compression by straight line programs (SLP). The variables of the string pattern can be instantiated by single characters. This is a generalisation of the fully compressed pattern match, which is the task of finding a compressed string in another compressed string, which is known to have a polynomial ti...

Let C = (C1, . . . , Cm) be a system of sets. The range of an injective partial choice function from C is called a rainbow set, and is also said to be multicolored by C. If φ is such a partial choice function and i ∈ dom(φ) we say that Ci colors φ(i) in the rainbow set. If the elements of Ci are sets then a rainbow set is said to be a (partial) rainbow matching if its range is a matching, namel...