The Bounded Cycle-Cover Problem

We consider the bounded cycle-cover problem, which is to find a minimum cost cycle cover of a two-connected graph such that no cycle in the cover contains more than a prescribed numbered of edges. This problem arises in the design of fiber-optic telecommunications networks that employ multiple self-healing rings to provide routing for communication traffic, even in the event of a fiber cut or other type of link failure. We present this problem, along with several related problems, and develop heuristic algorithms that find near optimal solutions for the bounded cycle-cover problem based on solution techniques for these related problems. Empirical results of these algorithms, applied to randomly generated problem instances, are presented and discussed.

[1]  Kemal Altinkemer,et al.  Using a Hop-Constrained Model to Generate Alternative Communication Network Design , 2015, INFORMS J. Comput..

[2]  Iraj Saniee,et al.  An optimization problem related to balancing loads on SONET rings , 1994, Telecommun. Syst..

[3]  Optimization Based Algorithms for Finding Minimal Cost Ring Covers in Survivable Networks , 1999, Comput. Optim. Appl..

[4]  Chun-Hsien Chen,et al.  The Capacity Comparison and Cost Analyses for SONET Self-Healing Ring Networks , 1994 .

[5]  Manuel Laguna,et al.  Clustering for the design of SONET rings in interoffice telecommunications , 1994 .

[6]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

[7]  Carsten Thomassen.  On the Complexity of Finding a Minimum Cycle Cover of a Graph , 1997, SIAM J. Comput..

[8]  Alon Itai,et al.  Covering a Graph by Circuits , 1978, ICALP.

[9]  Cun-Quan Zhang.  Integer Flows and Cycle Covers of Graphs , 1997 .

[10]  Iraj Saniee,et al.  SONET Toolkit: A Decision Support System for Designing Robust and Cost-Effective Fiber-Optic Networks , 1995 .

[11]  Herbert Fleischner,et al.  Eulersche linien und Kreisüberdeckungen, die vorgegebene durchgänge in den Kanten vermeiden , 1980, J. Comb. Theory, Ser. B.

[12]  Richard J. Lipton,et al.  Covering Graphs by Simple Circuits , 1981, SIAM J. Comput..

[13]  Jack Edmonds,et al.  Matching, Euler tours and the Chinese postman , 1973, Math. Program..

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  David Maxwell Chickering,et al.  On Finding a Cycle Basis with a Shortest Maximal Cycle , 1995, Inf. Process. Lett..

[16]  Wayne D. Grover,et al.  An algorithm for survivable network design employing multiple self-healing rings , 1993, Proceedings of GLOBECOM '93. IEEE Global Telecommunications Conference.

[17]  Tsong-Ho Wu,et al.  Fiber Network Service Survivability , 1992 .

[18]  Mauro Dell'Amico,et al.  Exact solution of the SONET Ring Loading Problem , 1999, Oper. Res. Lett..

[19]  Brian Alspach,et al.  Graphs with the circuit cover property , 1994 .

[20]  Joseph Douglas Horton,et al.  A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph , 1987, SIAM J. Comput..