An improved transitive closure algorithm

Computing ◽  
1983 ◽  
Vol 30 (4) ◽  
pp. 359-371 ◽  
Author(s):  
L. Schmitz
Keyword(s):  
Transitive Closure ◽  
Closure Algorithm

scholarly journals Fully Dynamic Transitive Closure in Plane Dags with one Source and one Sink

1994 ◽  
Vol 1 (30) ◽  
Author(s):  
Thore Husfeldt
Keyword(s):  
Transitive Closure ◽  
Upper Bounds ◽  
Directed Acyclic Graphs ◽  
Closure Problem ◽  
Directed Path ◽  
Lower And Upper Bounds ◽  
New Techniques ◽  
Time Dynamic ◽  
Acyclic Graphs ◽  
Closure Algorithm

We give an algorithm for the Dynamic Transitive Closure Problem for planar directed acyclic graphs with one source and one sink. The graph can be updated in logarithmic time under arbitrary edge insertions and deletions that preserve the embedding. Queries of the form `is there a directed path from u to v ?' for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges.<br /> <br />The result enlarges the class of graphs for which a logarithmic (or even polylogarithmic) time dynamic transitive closure algorithm exists. Previously, the only algorithms within the stated resource bounds put restrictions on the topology of the graph or on the delete operation. To obtain our result, we use a new characterisation of the transitive closure in plane graphs with one source and one sink and introduce new techniques to exploit this characterisation.<br /> <br />We also give a lower bound of Omega(log n/log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size. This is the first dynamic directed graph problem with almost matching lower and upper bounds.

scholarly journals Transitive closure algorithm MEMTC and its performance analysis

2001 ◽  
Vol 110 (1) ◽  
pp. 77-84 ◽  
Author(s):  
Vesa Hirvisalo ◽  
Esko Nuutila ◽  
Eljas Soisalon-Soininen
Keyword(s):  
Performance Analysis ◽  
Transitive Closure ◽  
Closure Algorithm

scholarly journals Algorithm for Multi- objective Traveling Salesman Problems based on Modified Transitive closure

2019 ◽  
Vol 9 (2) ◽  
pp. 2576-2581 ◽  
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Transitive Closure ◽  
Traveling Salesman ◽  
Traveling Salesman Problems ◽  
Numerical Examples ◽  
Multi Objective ◽  
Closure Method ◽  
Closure Algorithm

One of the challenging facts of the Multi Objective Traveling Salesman Problem (MOTSP) is to find the best compromised solution. In this paper, we have proposed a modified transitive closure algorithm to solve MOTSP using Genetic Algorithm (GA). Modified Transitive Closure method generates all the initial solutions of each objective. By applying Genetic Algorithm (GA), compromised solutions are obtained. Numerical examples are provided to show the efficiency of the proposed algorithm for MOTSP

scholarly journals Parallel transitive closure algorithm

2012 ◽  
Vol 19 (2) ◽  
pp. 161-166 ◽  
Author(s):  
C. E. R. Alves ◽  
E. N. Cáceres ◽  
A. A. de Castro ◽  
S. W. Song ◽  
J. L. Szwarcfiter
Keyword(s):  
Transitive Closure ◽  
Closure Algorithm
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