scholarly journals On the restrictive channel thickness estimation

2007 ◽  
Vol 20 (3) ◽  
pp. 499-506
Author(s):  
Iskandar Karapetyan
Keyword(s):  
Positive Integer ◽  
Heuristic Algorithms ◽  
Clique Number ◽  
Directed Path ◽  
Channel Routing ◽  
Routing Problem ◽  
Thickness Estimation ◽  
Channel Thickness ◽  
Np Complete ◽  
Routing Method

Channel routing is an important phase of physical design of LSI and VLSI chips. The channel routing method was first proposed by Akihiro Hashimoto and James Stevens [1]. The method was extensively studied by many authors and applied to different technologies. At present there are known many effective heuristic algorithms for channel routing. A. LaPaugh [2] proved that the restrictive routing problem is NP-complete. In this paper we prove that for every positive integer k there is a restrictive channel C for which ?(C)>? (HG)+L(VG)+k, where ? (C) is the thickness of the channel, ?(HG) is clique number of the horizontal constraints graph HG and L(VG) is the length of the longest directed path in the vertical constraints graph VG.

A Discrete Artificial Bee Colony Algorithm for the Reverse Logistics Location and Routing Problem

2017 ◽  
Vol 16 (05) ◽  
pp. 1339-1357 ◽  
Author(s):  
Kun Guo ◽  
Qishan Zhang
Keyword(s):  
Reverse Logistics ◽  
Vehicle Routing Problem ◽  
Artificial Bee Colony ◽  
Heuristic Algorithms ◽  
Routing Problem ◽  
Waste Products ◽  
Location Allocation ◽  
Bee Colony ◽  
Np Complete ◽  
Location Allocation Problem

Reverse logistics (RL) emerges as a hot topic in both research and business with the increasing attention on the collection and recycling of the waste products. Since Location and Routing Problem (LRP) in RL is NP-complete, heuristic algorithms, especially those built upon swarm intelligence, are very popular in this research. In this paper, both Vehicle Routing Problem (RP) and Location Allocation Problem (LAP) of RL are considered as a whole. First, the features of LRP in RL are analyzed. Second, a mathematical model of the problem is developed. Then, a novel discrete artificial bee colony (ABC) algorithm with greedy adjustment is proposed. The experimental results show that the new algorithm can approach the optimal solutions efficiently and effectively.

A HYBRID EVOLUTIONARY ALGORITHM FOR MULTIPLE-DESTINATIONS ROUTING PROBLEM

2004 ◽  
Vol 04 (04) ◽  
pp. 337-353 ◽  
Author(s):  
SALAH AL-SHARHAN ◽  
FAWAZ AL-ANZI
Keyword(s):  
Evolutionary Algorithm ◽  
Incremental Learning ◽  
Heuristic Algorithms ◽  
Learning Algorithm ◽  
Population Based ◽  
Multicast Tree ◽  
Routing Problem ◽  
Hybrid Evolutionary Algorithm ◽  
Np Complete ◽  
Qos Metrics

This paper presents a hybrid evolutionary algorithm for constrained multiple destinations routing problem. The problem can be formulated as minimising tree cost under several constraints or QoS metrics. Computing such constrained multicast tree has been proven to be NP-complete. The proposed hybrid algorithm is based on a population based incremental learning algorithm and a constrained distance network heuristic (or CKMB) algorithm. In the proposed algorithm, CKMB is utilised as a decoding scheme. Experimental results show that, in most cases, the proposed algorithm yields better solutions than other heuristic algorithms proposed in the literature including the best known one BSMA.

A Multilevel Pseudo-Boolean Satisfiability-Based Approach for Segmented Channel Routing

2015 ◽  
Vol 24 (06) ◽  
pp. 1550083
Author(s):  
Dahua Zhang ◽  
Wei Li ◽  
Tao Du
Keyword(s):  
Optimization Technique ◽  
Field Programmable Gate Arrays ◽  
Boolean Satisfiability ◽  
Channel Routing ◽  
Routing Problem ◽  
Gate Arrays ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Np Complete ◽  
Boolean Optimization

The segmented channel routing problem is fundamental to the routing of row-based field programmable gate arrays (FPGAs) and is proven to be nondeterministic polynomial time (NP) complete. In this paper, we capitalize on the compelling advancements in satisfiability (SAT) solvers to propose a multilevel pseudo-Boolean SAT-based approach. We construct several levels of hierarchy amongst the nets and the routing problem of each level is formulated as a pseudo-Boolean optimization (PBO) problem. Moreover, an optimization technique of reducing the number of variables in PBO problems is described to improve the scalability of the proposed method. Similar to the SAT-based routing, the unroutability of a given circuit can be proved by the approach. Experimental results show that the proposed method compares very favorably with existing algorithms and achieves the best convergence rate.

scholarly journals An Optimum Channel Routing Algorithm in the Knock-knee Diagonal Model

VLSI Design ◽  
1994 ◽  
Vol 1 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Xiaoyu Song
Keyword(s):  
Routing Algorithm ◽  
Difficult Problem ◽  
Layout Design ◽  
Channel Routing ◽  
Routing Problem ◽  
Vlsi Layout ◽  
Channel Density ◽  
Optimum Algorithm ◽  
Important Time ◽  
Optimum Channel

Channel routing problem is an important, time consuming and difficult problem in VLSI layout design. In this paper, we consider the two-terminal channel routing problem in a new routing model, called knock-knee diagonal model, where the grid consists of right and left tracks displayed at +45° and –45°. An optimum algorithm is presented, which obtains d + 1 as an upper bound to the channel width, where d is the channel density.

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