In this paper we study the following problem: Given n strings s1; s2; : : : ; sn, each of length m, nd a substring ti of length L for each si, and a string s of length L, such that max n i=1 d(s; ti) is minimized, where d(;) is the Hamming distance. The problem was raised in 6] in an application of genetic drug target search and is a key open problem in many applications 7]. The authors of 6] s...

Estimating the degree of approximation in the uniform norm, of a convex function on a finite interval, by convex algebraic polynomials, has received wide attention over the last twenty years. However, while much progress has been made especially in recent years by, among others, the authors of this article, separately and jointly, there have been left some interesting open questions. In this pa...

Some new methods for obtaining the minimax polynomial approximation of degree n to a continuous function are introduced, and applied to several simple functions. The amount of computation required is substantially reduced compared with that of previous methods.

Let Π be an NP-hard optimization problem, and let A be an approximation algorithm for Π. For an instance I of Π, let A(I) denote the objective value when running A on I, and let OPT (I) denote the optimal objective value. The approximation ratio of A for the instance I is RA(I) = A(I)/OPT (I), thus, when Π is minimization (maximization) problem RA(I) ≥ 1 (RA(I) ≤ 1). A polynomial time approxima...

The most common approach for approximating non-periodic function defined on a finite interval is based on considering polynomials as basis functions. In this paper we will address the non-optimallity of polynomial approximation and suggest to switch from powers of x to powers of sin(px) where p is a parameter which depends on the dimension of the approximating subspace. The new set does not suf...

• Assume that the input is random, and find an algorithm that will perform well in the average case. For example, the maximum clique problem, which is NP -hard, can actually be solved efficiently assuming a random input because the maximum clique in a randomly chosen graph is small. This assumption is often used in practice, but the problem is that not everyone will agree on whether the input d...