We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k) · n) for any function f of k and constant c independent of k. The problem can therefore be expected to be i...

We initiate the study of the smoothed complexity of the Closest String problem by proposing a semi-random model of Hamming distance. We restrict interest to the optimization version of the Closest String problem, and give a 2-approximation algorithm, which we refer to as CSP-Greedy, that runs in O(n` + `)-time, where ` is the string length and n is the number of strings. Using smoothed analysis...

We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k) · n) for any function f of k and constant c independent of k. The problem can therefore be expected to be i...

The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A variant of SVP (commonly studied in computatio...

in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...

Voltage collapse and blackout can occur in an electric power system when load powers vary so that the system loses stability in a saddle node bifurcation. We propose new iterative and direct methods to compute load powers a t which bifurcation occurs and which are locally closest to the current operating load powers. The distance in load power parameter space to this locally closest bifurcation...