Decomposition algorithms for solving the minimum weight maximal matching problem

Networks ◽  
2013 ◽  
Vol 62 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Merve Bodur ◽  
Tinaz Ekim ◽  
Z. Caner Taşkin
Keyword(s):  
Minimum Weight ◽  
Decomposition Algorithms ◽  
Matching Problem ◽  
Maximal Matching

Optimization of Multiple Head SMT Placement Machine: Model and Approaches

2002 ◽  
Author(s):  
Youjiao Zeng ◽  
Junqi Yan ◽  
Ye Jin ◽  
Tao Jiang
Keyword(s):  
Printed Circuit Board ◽  
Travelling Salesman Problem ◽  
Minimum Weight ◽  
Optimal Solution ◽  
Circuit Board ◽  
Matching Problem ◽  
Machine Model ◽  
Head Surface ◽  
Pick And Place ◽  
Placement Machine

In order to maximize the throughput rate of single multiple head surface mounted technology placement machine, the time taken for pick-and-place of components for each printed circuit board has to be minimized. This gives rise to two related essential problems, namely feeder assignment problem and pick-and-place sequence determination problem. In this paper, we introduce a model that simplifies problems. We regard all components during a pick-and-place cycle as a unit and give it a matching weight. In this way, we change multiple head machine problems into single head machine problems. The optimisation problem becomes two sub-problems: minimum weight matching problem and travelling salesman problem of these units. We presented algorithms to obtain near optimal solution and implement them as a computer program. We performed experiment on a real four head placement machine. The experimental results are presented to analyse their performance.

DNA Computing Algorithm to Solve the Least Maximal Matching Problem

2015 ◽  
Vol 12 (9) ◽  
pp. 2348-2351
Author(s):  
Lingmin Zhang ◽  
Dongmei Huang ◽  
Wang Wang ◽  
Ji Zuwen
Keyword(s):  
Dna Computing ◽  
Matching Problem ◽  
Maximal Matching ◽  
Computing Algorithm

A DNA Algorithm for the maximal matching problem

2015 ◽  
Vol 76 (10) ◽  
pp. 1797-1802 ◽  
Author(s):  
Wenxia Li ◽  
E. M. Patrikeev ◽  
Dongmei Xiao
Keyword(s):  
Matching Problem ◽  
Maximal Matching ◽  
Dna Algorithm

scholarly journals HEURISTIC SEARCH IN CONSTRAINED BIPARTITE MATCHING WITH APPLICATIONS TO PROTEIN NMR BACKBONE RESONANCE ASSIGNMENT

2005 ◽  
Vol 03 (06) ◽  
pp. 1331-1350 ◽  
Author(s):  
GUOHUI LIN ◽  
THEODORE TEGOS ◽  
ZHI-ZHONG CHEN
Keyword(s):  
Resonance Assignment ◽  
Complete Bipartite Graph ◽  
Minimum Weight ◽  
Protein Nmr ◽  
The Other ◽  
Backbone Resonance Assignment ◽  
Matching Problem ◽  
Bipartite Matching ◽  
Backbone Resonance ◽  
Directed Paths

The constrained bipartite matching (CBM) problem is a variant of the classical bipartite matching problem that has been well studied in the Combinatorial Optimization community. The input to CBM is an edge-weighted complete bipartite graph in which there are a same number of vertices on both sides and vertices on one side are sequentially ordered while vertices on the other side are partitioned and connected into disjoint directed paths. In a feasible matching, a path must be mapped to consecutive vertices on the other side. The optimization goal is to find a maximum or a minimum weight perfect matching. Such an optimization problem has its applications to scheduling and protein Nuclear Magnetic Resonance peak assignment. It has been shown to be NP-hard and MAX SNP-hard if the perfectness requirement is dropped. In this paper, more results on the inapproximability are presented and IDA*, a memory efficient variant of the well known A* search algorithm, is utilized to solve the problem. Accordingly, search heuristics and a set of heuristic evaluation functions are developed to assist the search, whose effectiveness is demonstrated by a simulation study using real protein NMR backbone resonance assignment instances.

scholarly journals Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time

2015 ◽  
Vol 15 (1&2) ◽  
pp. 145-158
Author(s):  
Austin G. Fowler
Keyword(s):  
Error Correction ◽  
Perfect Matching ◽  
Fault Tolerant ◽  
Minimum Weight ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Matching Problem ◽  
Topological Quantum ◽  
Square Array ◽  
Quantum Error

Consider a 2-D square array of qubits of extent $L\times L$. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be exactly solved with a 2-D square array of classical computing devices, each of which is nominally associated with a fixed number $N$ of qubits, in constant average time per round of error detection independent of $L$ provided physical error rates are below fixed nonzero values, and other physically reasonable assumptions. This proof is applicable to the fully fault-tolerant case only, not the case of perfect stabilizer measurements.

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