Applying River Formation Dynamics to Solve NP-Complete Problems

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a "short" quantum proof; more precisely, NP\subseteq QMA_{\log}(2) where QMA_{\log}(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP\subseteq QMA_{\log}(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthur protocol for 3-coloring with perfect completeness and gap 1/24n^6. Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering $\widetilde{O}(\sqrt{n})$ witnesses of logarithmic size. However, we still do not know if QMA_{\log}(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMA_{\log}(2) protocol with the gap 1/n^{3+\epsilon}} for every constant \epsilon>0.

Download Full-text

Towards Solving NP-Complete Problems by Using a Molecular Supercomputer Model

New Horizons of Parallel and Distributed Computing ◽

10.1007/0-387-28967-4_5 ◽

2006 ◽

pp. 67-79

Author(s):

Minyi Guo ◽

Weng-Long Chang

Keyword(s):

Complete Problems ◽

Np Complete

Download Full-text

Minimizing area of VLSI power distribution networks using river formation dynamics

Journal of Systems and Information Technology ◽

10.1108/jsit-10-2017-0097 ◽

2018 ◽

Vol 20 (4) ◽

pp. 417-429 ◽

Cited By ~ 3

Author(s):

Satyabrata Dash ◽

Sukanta Dey ◽

Deepak Joshi ◽

Gaurav Trivedi

Keyword(s):

Power Distribution ◽

Large Scale ◽

Distribution Network ◽

Distribution Networks ◽

Power Distribution Networks ◽

Power Distribution Network ◽

Content Type ◽

Ir Drop ◽

Formation Dynamics ◽

River Formation Dynamics

Purpose The purpose of this paper is to demonstrate the application of river formation dynamics to size the widths of power distribution network for very large-scale integration designs so that the wire area required by power rails is minimized. The area minimization problem is transformed into a single objective optimization problem subject to various design constraints, such as IR drop and electromigration constraints. Design/methodology/approach The minimization process is carried out using river formation dynamics heuristic. The random probabilistic search strategy of river formation dynamics heuristic is used to advance through stringent design requirements to minimize the wire area of an over-designed power distribution network. Findings A number of experiments are performed on several power distribution benchmarks to demonstrate the effectiveness of river formation dynamics heuristic. It is observed that the river formation dynamics heuristic outperforms other standard optimization techniques in most cases, and a power distribution network having 16 million nodes is successfully designed for optimal wire area using river formation dynamics. Originality/value Although many research works are presented in the literature to minimize wire area of power distribution network, these research works convey little idea on optimizing very large-scale power distribution networks (i.e. networks having more than four million nodes) using an automated environment. The originality in this research is the illustration of an automated environment equipped with an efficient optimization technique based on random probabilistic movement of water drops in solving very large-scale power distribution networks without sacrificing accuracy and additional computational cost. Based on the computation of river formation dynamics, the knowledge of minimum area bounded by optimum IR drop value can be of significant advantage in reduction of routable space and in system performance improvement.

Download Full-text