This problem is also NP-hard; yet, there is a (1.5 + epsilon)-approximation algorithm that uses rounding and grouping by rounding the sizes of the items to powers of (1 + epsilon) and then ...

Abstract: In this paper, we investigate a network synthesis problem that aims to improve the performance of noisy linear consensus networks by establishing a few new interconnection links throughout ...

NP-hard: A classification for problems for which no polynomial-time algorithm is known, implying that a solution may require non-polynomial resources in the worst case.

most of them are based on some problem-specific heuristic. A heuristic is a common-sense rule drawn from experience rather than from a mathematically proved assertion. For example, going to the ...

Learn some strategies to cope with NP-completeness and find good solutions for hard optimization problems, such as approximation, heuristic, randomized, parameterized, and metaheuristic algorithms.

The Stanford researchers apply Grover’s algorithm to the number partitioning problem by encoding each possible partition of the integer list as a quantum state. They also formulate an oracle that can ...

Due to the NP-hardness of the problem, finding practical solutions relies on approximation algorithms. The central point of this research is to develop effective models and mechanisms that approximate ...

Next, we will study algorithms for NP-hard problems whose solutions are guaranteed to be within some approximation factor of the best possible solutions. Such algorithms are often quite efficient and ...

In this paper, we investigate a network synthesis problem that aims to improve the performance of noisy linear consensus networks by establishing a few new interconnection links throughout the network ...