The application of Steiner trees to delay constrained multicast routing: a tabu search approach

Abstract

Ahstrncl-With today's development of information technologycomes the increased development of numerous real-time multimedia network applications. Some examples include video and tele-confereneing, tele-medicine. video-on-demand, distance education, applications in finance, etc. Several of these applications require multicasting with a certain Quality of Service (QoS). One of the most important QoS parametcrs is the maximum end-to-end delay from the source to any destination in a multicast session. This paper deals with the problem of DelayConstrained Multicast Routing (DCMR). The DCMR problem cm be reduced to the constrained Minimum Steiner Tree Problem in Graphs (CMStTG). Since the Minimum Steiner Tree Problem in Graphs (MStTG) has been proven to be NP-complete, several heuristics have been developed for solving hlStTG and CMStTG. I n this paper, we suggest a tabu search heuristic for the DChlR problem. This heuristic was developed on the basis of a tabu search heuristic designed for solving unconstrained minimum Steiner tree problems. Preliminary testing on drta from B publicly available library, StcinLib, has shown that this heuristic gives near optimal solutions in moderate time and a moderate number o f iterations for medium sized problems (SO-100 nodes). Comparing with B well known algorithm for solving the ChlStTG problem, tests have shown that our tabu search heuristic is superior in quality for medium sized problems.

An iterative local search approach based on fitness landscapes analysis for the delay-constrained multicast routing problem

“…In addition to the above mentioned simple greedy local search in Figure 1 (hereinafter named LS), we re-implement three other local search heuristics, namely BSMA [45], TS-CST [44] and VNDMR [13] in the literature, for solving the DCLC-MRP with different delay constraints. We give the brief description of the three local search heuristics as follows:…”

“…For a multicast tree in the network of n bits with a source node and |D| destination nodes in the multicast group, the number of possible neighboring solutions of the current multicast tree is bounded by n -|D| -1. This node-based neighborhood operator has also been applied in [44,11]. It is known that higher values of fdc correlation ρ indicate that the fitness value and distance of solutions to x opt in the search space are correlated and thus the problem presents to be easier for search algorithms.…”

“…As the source and all destination nodes must be included in a multicast tree, the value of their corresponding bits in the binary vector (of a feasible solution) should always be 1. This simple binary vector has been widely used in the literature and shows to be simple yet effective for representing a multicast tree [44,11].…”

“…To prevent the heuristic from oscillating between neighboring solutions, a tabu list of length one is updated to remember the corresponding bit in the last performed move. The process stops after a pre-defined number of iterations without improvements, set to 2 in [44].…”

“…The TS-CST algorithm in [44] is developed based on a tabu search, where a binary vector solution representation has been used (and adapted in our study here, see Section 4.2 above). A solution (a multicast tree) is represented by a binary set of |V \ ({s}  D)| bits, each corresponding to a node in V \ ({s}  D).…”