A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...

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...

Preplaced circuit modules may be rotated to improve performance and/or routability. We show that several simple versions of the module rotation problem are NP-hard.

University of Florida Technical Report 91-29 Abstract Graphs with delays associated with their edges are often used to model communication and signal flow networks. Network performance can be improved by upgrading the network vertices. Such an improvement reduces the edge delays and comes at a cost. We study different formulations of this network performance improvement problem and show that th...

A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...

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 travelling salesmen problem (tsp) is one of the most important and famous combinational optimization problems that aim to find the shortest tour. in this problem, the salesman starts to move from an arbitrary place called depot and after visiting all nodes, finally comes back to depot. solving this problem seems hard because program statement is simple and leads this problem belonging to np...

the traveling salesman problem (tsp) is a well-known combinatorial optimization problem and holds a central place in logistics management. the tsp has received much attention because of its practical applications in industrial problems. many exact, heuristic and metaheuristic approaches have been proposed to solve tsp in recent years. in this paper, a modified ant colony optimization (maco) is ...