The Edge Group Coloring Problem with Applications to Multicast Switching

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the performance of several approximation algorithms, both analytically and experimentally. We find that for random $\chi$-colorable graphs, the number of colors used by the best algorithms falls within a small constant factor of $\chi$, where the constant factor is mainly a function of the ratio of the number of outputs to inputs. When this ratio is less than 10, the best algorithms produces solutions that use fewer than $2\chi$ colors. In addition, one of the algorithms studied finds high quality approximate solutions for any graph with high probability, where the probability of a low quality solution is a function only of the random choices made by the algorithm

The Edge Group Coloring Problem with Applications to Multicast Switching

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the performance of several approximation algorithms, both analytically and experimentally. We find that for random χ-colorable graphs, the number of colors used by the best algorithms falls within a small constant factor of χ, where the constant factor is mainly a function of the ratio of the number of outputs to inputs. When this ratio is less than 10, the best algorithms produces solutions that use fewer than 2χ colors. In addition, one of the algorithms studied finds high quality approximate solutions for any graph with high probability, where the probability of a low quality solution is a function only of the random choices made by the algorithm

Analyzing Traffic and Multicast Switch Issues in an ATM Network.

This dissertation attempts to solve two problems related to an ATM network. First, we consider packetized voice and video sources as the incoming traffic to an ATM multiplexer and propose modeling methods for both individual and aggregated traffic sources. These methods are, then, used to analyze performance parameters such as buffer occupancy, cell loss probability, and cell delay. Results, thus obtained, for different buffer sizes and number of voice and video sources are analyzed and compared with those generated from existing techniques. Second, we study the priority handling feature for time critical services in an ATM multicast switch. For this, we propose a non-blocking copy network and priority handling algorithms. We, then, analyze the copy network using an analytical method and simulation. The analysis utilizes both priority and non-priority cells for two different output reservation schemes. The performance parameters, based on cell delay, delay jitter, and cell loss probability, are studied for different buffer sizes and fan-outs under various input traffic loads. Our results show that the proposed copy network provides a better performance for the priority cells while the performance for the non-priority cells is slightly inferior in comparison with the scenario when the network does not consider priority handling. We also study the fault-tolerant behavior of the copy network, specially for the broadcast banyan network subsection, and present a routing scheme considering the non-blocking property under a specific pattern of connection assignments. A fault tolerant characteristic can be quantified using the full access probability. The computation of the full access probability for a general network is known to be NP-hard. We, therefore, provide a new bounding technique utilizing the concept of minimal cuts to compute full access probability of the copy network. Our study for the fault-tolerant multi-stage interconnection network having either an extra stage or chaining shows that the proposed technique provides tighter bounds as compared to those given by existing approaches. We also apply our bounding method to compute full access probability of the fault-tolerant copy network