On the quality of graphs generated by swarm algorithms

Swarm algorithms are often used for the generation of graphs. The generated graphs are mostly planar, inexpensive and fault-tolerant. In this work we evaluate the graphs produced by a swarm algorithm with respect to the properties and the quality of the found graphs and to the runtime requirements. The algorithm under consideration is essentially a simulation of the foraging of the slime mold Physarum polycephalum. Especially emphasized are the properties of the algorithm, since its deployment in many other works is limited to the existence of a graph solution, not reporting however the quality of the graph and runtime requirements of the algorithm. We compare the quality of the resulting graphs and the runtime of the algorithm to classical algorithms from graph theory. Our results show that the slime mold algorithm has some interesting features, however it is not the best means to construct graphs of large sets of nodes in terms of efficiency of the algorithm or quality of the outcome.

[1]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[2]  Andrew Adamatzky,et al.  Developing Proximity Graphs by Physarum polycephalum: Does the Plasmodium Follow the Toussaint Hierarchy? , 2009, Parallel Process. Lett..

[3]  Matthias Becker,et al.  On the Efficiency of Nature-Inspired Algorithms for Generation of Fault-Tolerant Graphs , 2015, 2015 IEEE International Conference on Systems, Man, and Cybernetics.

[4]  Kenneth J. Supowit,et al.  The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees , 1983, JACM.

[5]  Jeff Jones,et al.  Programmable reconfiguration of Physarum machines , 2009, Natural Computing.

[6]  Giri Narasimhan,et al.  Geometric spanner networks , 2007 .

[7]  D. Kirkpatrick,et al.  A Framework for Computational Morphology , 1985 .

[8]  Helena Szczerbicka,et al.  Applicability of Bio-inspired and Graph-Theoretic Algorithms for the Design of Complex Fault-Tolerant Graphs , 2013, 2013 IEEE International Conference on Systems, Man, and Cybernetics.

[9]  Colin Barras.  What a maze-solving oil drop can tell us about intelligence , 2010 .

[10]  Xiang-Yang Li,et al.  Power efficient and sparse spanner for wireless ad hoc networks , 2001, Proceedings Tenth International Conference on Computer Communications and Networks (Cat. No.01EX495).

[11]  Jeff Jones.  Approximating the Behaviours of Physarum polycephalum for the Construction and Minimisation of Synthetic Transport Networks , 2009, UC.

[12]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[13]  Jeff Jones,et al.  The Emergence and Dynamical Evolution of Complex Transport Networks from Simple Low-Level Behaviours , 2015, Int. J. Unconv. Comput..

[14]  Helena Szczerbicka,et al.  Comparison of Bio-Inspired and Graph-Theoretic Algorithms for Design of Fault-Tolerant Networks , 2012, ICAS 2012.

[15]  David G. Kirkpatrick,et al.  On the Spanning Ratio of Gabriel Graphs and beta-skeletons , 2002, LATIN.

[16]  Kenneth Sörensen,et al.  Metaheuristics - the metaphor exposed , 2015, Int. Trans. Oper. Res..

[17]  Jukka Teuhola,et al.  A Linear Expected-Time Algorithm for Computing Planar Relative Neighbourhood Graphs , 1987, Inf. Process. Lett..

[18]  T. Nakagaki,et al.  Intelligence: Maze-solving by an amoeboid organism , 2000, Nature.

[19]  Madeleine Beekman,et al.  Solving the Towers of Hanoi – how an amoeboid organism efficiently constructs transport networks , 2013, Journal of Experimental Biology.

[20]  Matthias Becker.  Design of fault tolerant networks with agent-based simulation of Physarum polycephalum , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[21]  A. Tero,et al.  Rules for Biologically Inspired Adaptive Network Design , 2010, Science.

[22]  Andrew Adamatzky,et al.  A Would-Be Nervous System Made from a Slime Mold , 2015, Artificial Life.

[23]  David P. Dobkin,et al.  On sparse spanners of weighted graphs , 1993, Discret. Comput. Geom..