Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

the scheduling problems are the non-polynomial problems-hard (np-hard), is to solve it, and meta-heuristic innovative method compared with the exact method require less time and memory.in this research, developed imperialistic competitive algorithm used to solving the single-mode resource-constrained project scheduling problem.also the basic feasible solution algorithm used in order to increase...

We propose a new branch-and-bound algorithm to solve hard instances of set covering problems arising from Steiner triple systems.

We present a detailed experimental investigation of the easy-hard-easy phase transition for randomly generated instances of satisfiability problems. Problems in the hard part of the phase transition have been extensively used for benchmarking satisfiability algorithms. This study demonstrates that problem classes and regions of the phase transition previously thought to be easy can sometimes be...

We consider the problem of synthesizing feasible signals in the presence of inconsistent convex constraints, some of which are hard in the sense that they must absolutely be satis ed. This problem is formalized as that of minimizing an objective function measuring the degree of unfeasibility with respect to the soft constraints over the intersection of the sets associated with the hard constrai...

We prove exponential lower bounds on the running time of many algorithms for Constraint Satisfaction, by giving a simple family of instances on which they always take exponential time. Although similar lower bounds for most of these algorithms have been shown before, we provide a uniform treatment which illustrates a powerful general approach and has stronger impfications for the practice of al...

In this thesis, we use and refine methods of computational complexity theory to analyze the complexity of sparse instances, such as graphs with few edges or formulas with few constraints of bounded width. Two natural questions arise in this context: • Is there an efficient algorithm that reduces arbitrary instances of an NP-hard problem to equivalent, sparse instances? • Is there an algorithm t...

We consider the classical vertex cover and set cover problems with the addition of hard capacity constraints. This means that a set (vertex) can only cover a limited number of its elements (adjacent edges) and the number of available copies of each set (vertex) is bounded. This is a natural generalization of the classical problems that also captures resource limitations in practical scenarios. ...

In computational geometry, packing problems ask whether a set of rigid pieces can be placed inside a target region such that no two pieces overlap. The triangle packing problem is a packing problem that involves triangular pieces, and it is crucial for algorithm design in many areas, including origami design, cutting industries, and warehousing. Previous works in packing algorithms have conject...

The Closest Substring Problem is one of the most important problems in the field of computational biology. It is stated as follows: given a set of t sequences s1; s2; : : : st over an alphabet , and two integers k; d with d k, can one find a string s of length k and, for all i = 1; 2; : : : ; t, substrings oi of si, all of length k, such that d(s; oi) d (for all i = 1; 2; : : : ; t)? (here, d(:...