scholarly journals On an asymptotic optimization problem in finite, directed, weighted graphs

1968 ◽  
Vol 13 (6) ◽  
pp. 527-533 ◽  
Author(s):  
I.L. Traiger ◽  
A. Gill
Keyword(s):  
Optimization Problem ◽  
Weighted Graphs ◽  
Asymptotic Optimization ◽  
Directed Weighted Graphs

On Computing the Diameter of Real-World Directed (Weighted) Graphs

2012 ◽  
pp. 99-110 ◽  
Author(s):  
Pierluigi Crescenzi ◽  
Roberto Grossi ◽  
Leonardo Lanzi ◽  
Andrea Marino
Keyword(s):  
Real World ◽  
Weighted Graphs ◽  
Directed Weighted Graphs

scholarly journals Linear Time Additively Exact Algorithm for Transformation of Chain-Cycle Graphs for Arbitrary Costs of Deletions and Insertions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2001
Author(s):  
Konstantin Gorbunov ◽  
Vassily Lyubetsky
Keyword(s):  
Linear Time ◽  
Exact Algorithm ◽  
Time Algorithm ◽  
Additive Constant ◽  
Weighted Graphs ◽  
Total Cost ◽  
Operation Costs ◽  
Double Cut And Join ◽  
Vertex Degrees ◽  
Directed Weighted Graphs

We propose a novel linear time algorithm which, given any directed weighted graphs a and b with vertex degrees 1 or 2, constructs a sequence of operations transforming a into b. The total cost of operations in this sequence is minimal among all possible ones or differs from the minimum by an additive constant that depends only on operation costs but not on the graphs themselves; this difference is small as compared to the operation costs and is explicitly computed. We assume that the double cut and join operations have identical costs, and costs of the deletion and insertion operations are arbitrary strictly positive rational numbers.

Frequency Graphs for Travelling Salesman Problem Based on Ant Colony Optimization

2019 ◽  
Vol 18 (03) ◽  
pp. 1950016
Author(s):  
Yong Wang ◽  
Yiwen Wu
Keyword(s):  
Ant Colony Optimization ◽  
Optimization Problem ◽  
Hamiltonian Cycle ◽  
Travelling Salesman Problem ◽  
Weighted Graph ◽  
Ant Colony ◽  
The Other ◽  
Hamiltonian Cycles ◽  
Weighted Graphs ◽  
Better Than

Traveling salesman problem (TSP) is a typical combinatorial optimization problem. A heuristic model called frequency graph is introduced for TSP. It is computed with a set of optimal i-vertex paths (OP) in a weighted graph. The frequencies on the edges are enumerated from the set of OPs. The OPs have more intersections of edges with the optimal Hamiltonian cycle (OHC) than they do with the other Hamiltonian cycles. Thus, the frequencies of the OHC edges are generally bigger than those of most of the other edges. They are taken as the heuristic information instead of edges’ weights for TSP. The ant colony optimization is used to find an approximation or OHC based on the frequency graph. The solutions are compared with those using weighted graphs for certain TSP instances. The experimental results show that the frequency graph is better than weighted graph (WG) for most TSPs under the same preconditions.

scholarly journals A fast and robust kernel optimization method for core–periphery detection in directed and weighted graphs

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Francesco Tudisco ◽  
Desmond J. Higham
Keyword(s):  
Social Sciences ◽  
Graph Mining ◽  
Large Scale ◽  
Optimization Problem ◽  
Graph Model ◽  
Optimization Method ◽  
Weighted Graphs ◽  
Classification Problems ◽  
Random Graph Model ◽  
Kernel Optimization

Abstract Many graph mining tasks can be viewed as classification problems on high dimensional data. Within this class we consider the issue of discovering core-periphery structure, which has wide applications in the economic and social sciences. In contrast to many current approaches, we allow for weighted and directed edges and we do not assume that the overall network is connected. Our approach extends recent work on a relevant relaxed nonlinear optimization problem. In the directed, weighted setting, we derive and analyze a globally convergent iterative algorithm. We also relate the algorithm to a maximum likelihood reordering problem on an appropriate core-periphery random graph model. We illustrate the effectiveness of the new algorithm on a large scale directed email network.

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