Call Control in Rings

The call control problem is an important optimization problem encountered in the design and operation of communication networks. The goal of the call control problem in rings is to compute, for a given ring network with edge capacities and a set of paths in the ring, a maximum cardinality subset of the paths such that no edge capacity is violated. We give a polynomial-time algorithm to solve the problem optimally. The algorithm is based on a decision procedure that checks whether a solution with at least k paths exists, which is in turn implemented by an iterative greedy approach operating in rounds.We show that the algorithm can be implemented efficiently and, as a by-product, obtain a linear-time algorithm to solve the call control problem in chains optimally.

[1]  Jeremy P. Spinrad,et al.  An O(n2 algorithm for circular-arc graph recognition , 1993, SODA '93.

[2]  Robert E. Tarjan,et al.  A linear-time algorithm for a special case of disjoint set union , 1983, J. Comput. Syst. Sci..

[3]  Errol L. Lloyd,et al.  on the K-coloring of Intervals , 1991, Discrete Applied Mathematics.

[4]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[5]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for a Special Case of Disjoint Set Union , 1985, J. Comput. Syst. Sci..

[6]  I. A. Karapetian,et al.  On the coloring of circular arc graphs , 1980 .

[7]  Serge A. Plotkin.  Competitive Routing of Virtual Circuits in ATM Networks , 1995, IEEE J. Sel. Areas Commun..

[8]  Stefano Leonardi,et al.  On-line Network Routing , 1996, Online Algorithms.

[9]  Peter Winkler,et al.  Ring routing and wavelength translation , 1998, SODA '98.

[10]  Gary L. Miller,et al.  The Complexity of Coloring Circular Arcs and Chords , 1980, SIAM J. Algebraic Discret. Methods.

[11]  Errol L. Lloyd,et al.  On the k -coloring of intervals , 1995 .

[12]  Yossi Azar,et al.  Beating the Logarithmic Lower Bound: Randomized Preemptive Disjoint Paths and Call Control Algorithms , 1999, SODA '99.

[13]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[14]  Moti Yung,et al.  Efficient On-Line Call Control Algorithms , 1997, J. Algorithms.

[15]  Adam Tauman Kalai,et al.  Admission Control to Minimize Rejections , 2001, WADS.