Exact and approximate algorithms for the longest induced path problem

RAIRO - Operations Research ◽

10.1051/ro/2021004 ◽

2021 ◽

Author(s):

Celso C Ribeiro ◽

Ruslán G. Marzo

Keyword(s):

Computational Experiments ◽

Simple Path ◽

Approximate Algorithms ◽

Optimal Solutions ◽

Induced Path ◽

Enumerative Algorithm ◽

New Algorithms

The longest induced path problem consists in finding a maximum subset of vertices of a graph such that it induces a simple path. We propose a new exact enumerative algorithm that solves problems with up to 138 vertices and 493 edges and a heuristic for larger problems. Detailed computational experiments compare the results obtained by the new algorithms with other approaches in the literature and investigate the characteristics of the optimal solutions.

Download Full-text

An enumerative algorithm for computing all possibly optimal solutions to an interval LP

Top ◽

10.1007/s11750-012-0268-2 ◽

2012 ◽

Vol 22 (2) ◽

pp. 530-542 ◽

Cited By ~ 7

Author(s):

Carla Oliveira ◽

Carlos Henggeler Antunes ◽

Carlos Barrico

Keyword(s):

Optimal Solutions ◽

Enumerative Algorithm

Download Full-text

Computational experiments with a lazy version of a K quickest simple path ranking algorithm

Top ◽

10.1007/s11750-007-0033-0 ◽

2007 ◽

Vol 15 (2) ◽

pp. 372-382 ◽

Cited By ~ 7

Author(s):

M. Pascoal ◽

M. E. Captivo ◽

J. C. Clímaco

Keyword(s):

Computational Experiments ◽

Simple Path ◽

Ranking Algorithm

Download Full-text

Algorithms for Euclidean Degree Bounded Spanning Tree Problems

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195919500031 ◽

2019 ◽

Vol 29 (02) ◽

pp. 121-160 ◽

Cited By ~ 2

Author(s):

Patrick J. Andersen ◽

Charl J. Ras

Keyword(s):

Approximation Algorithms ◽

Spanning Tree ◽

Maximum Degree ◽

Euclidean Plane ◽

Minimum Spanning Tree ◽

Computational Experiments ◽

Optimal Solutions ◽

New Type ◽

Disjoint Sets ◽

Set Of Points

Given a set of points in the Euclidean plane, the Euclidean [Formula: see text]-minimum spanning tree ([Formula: see text]-MST) problem is the problem of finding a spanning tree with maximum degree no more than [Formula: see text] for the set of points such the sum of the total length of its edges is minimum. Similarly, the Euclidean [Formula: see text]-minimum bottleneck spanning tree ([Formula: see text]-MBST) problem, is the problem of finding a degree-bounded spanning tree for a set of points in the plane such that the length of the longest edge is minimum. When [Formula: see text], these two problems may yield disjoint sets of optimal solutions for the same set of points. In this paper, we perform computational experiments to compare the accuracies of a variety of heuristic and approximation algorithms for both these problems. We develop heuristics for these problems and compare them with existing algorithms. We also describe a new type of edge swap algorithm for these problems that outperforms all the algorithms we tested.

Download Full-text

An analysis between exact and approximate algorithms for the k-center problem in graphs

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v12i2.pp2058-2065 ◽

2022 ◽

Vol 12 (2) ◽

pp. 2058

Author(s):

Velin Kralev ◽

Radoslava Kraleva ◽

Viktor Ankov ◽

Dimitar Chakalov

Keyword(s):

Operating System ◽

Execution Time ◽

Source Code ◽

Exact Algorithm ◽

Approximate Solutions ◽

Approximate Algorithm ◽

Approximate Algorithms ◽

Optimal Solutions ◽

Center Problem ◽

Computation Complexity

<span lang="EN-US">This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm.</span>

Download Full-text

An Improved Vogel's Approximation Method for the Transportation Problem

Mathematical and Computational Applications ◽

10.3390/mca16020370 ◽

2011 ◽

Vol 16 (2) ◽

pp. 370-381 ◽

Cited By ~ 10

Author(s):

Serdar Korukoğlu ◽

Serkan Ballı

Keyword(s):

Approximation Method ◽

Operations Research ◽

Opportunity Cost ◽

Transportation Problem ◽

Large Scale ◽

Efficient Solutions ◽

Important Task ◽

Computational Experiments ◽

Optimal Solutions ◽

Transportation Problems

Determining efficient solutions for large scale transportation problems is an important task in operations research. In this study, Vogel’s Approximation Method (VAM) which is one of well-known transportation methods in the literature was investigated to obtain more efficient initial solutions. A variant of VAM was proposed by using total opportunity cost and regarding alternative allocation costs. Computational experiments were carried out to evaluate VAM and improved version of VAM (IVAM). It was seen that IVAM conspicuously obtains more efficient initial solutions for large scale transportation problems. Performance of IVAM over VAM was discussed in terms of iteration numbers and CPU times required to reach the optimal solutions.

Download Full-text

PARALLEL OPTIMIZATION TECHNOLOGY FOR ATOMIC-MOLECULAR MORSE CLUSTERS

Информационные и математические технологии в науке и управлении ◽

10.38028/esi.2021.24.4.006 ◽

2022 ◽

pp. 60-67

Author(s):

Александр Юрьевич Горнов ◽

Антон Сергеевич Аникин ◽

Павел Сергеевич Сороковиков ◽

Татьяна Сергеевна Зароднюк

Keyword(s):

Molecular Docking ◽

Software Package ◽

Molecular Clusters ◽

Computational Experiments ◽

Applied Problem ◽

Parallel Optimization ◽

Computing Technology ◽

Morse Clusters ◽

New Algorithms

В статье рассматриваются специализированные вычислительные технологии и алгоритмы, используемые для поиска низкопотенциальных атомно-молекулярных кластеров. Проведенные вычислительные эксперименты продемонстрировали достаточно высокую конкурентоспособность новых алгоритмов по сравнению с классическими для функций рассматриваемого типа. С использованием разработанного программного комплекса получены рекордные результаты оптимизации атомно-молекулярных кластеров Морса рекордных размерностей. The paper deals with specialized computing technology and algorithms used for finding low-potential atomic-molecular clusters. The performed computational experiments demonstrated a rather high competitiveness of the new algorithms in comparison with the classical methods for the considerable functions. Using the developed software, the applied problem of molecular docking was solved. Using the developed software package, record results for optimization of atomic-molecular Morse clusters of large dimensions have been obtained.

Download Full-text

Approximate Algorithms for Continuous-Time Quickest Multi-Commodity Contraflow Problem

The Nepali Mathematical Sciences Report ◽

10.3126/nmsr.v37i1-2.34068 ◽

2020 ◽

Vol 37 (1-2) ◽

pp. 30-46

Author(s):

Shiva Prakash Gupta ◽

Durga Prasad Khanal ◽

Urmila Pyakurel ◽

Tanka Nath Dhamala

Keyword(s):

Approximation Algorithms ◽

Polynomial Time ◽

Continuous Time ◽

Flow Problem ◽

Capacity Constraints ◽

Approximate Algorithms ◽

Optimal Solutions ◽

Commodity Flow ◽

Flow Problems

Multi-commodity flow problem appears when several distinct commodities are shipped from supply nodes to the demand nodes through a network without violating the capacity constraints. The quickest multi-commodity flow problem deals with the minimization of time satisfying given demand. Ingeneral, the quickest multi-commodity flow problems are computationally hard. The outbound lane capacities can be increased through reverting the orientation of lanes towards the demand nodes. We present two approximation algorithms by introducing partial contraow technique in the continuous-time quick estmulti-commodity ow problem: one polynomial-time with the help of length-bounded flow and another FPTAS by using _-condensed time-expanded graph. Both algorithms reverse only necessary arc capacities to get the optimal solutions and save unused arc capacities which may be used for other purposes.

Download Full-text