Bidirectional Multi-Constrained Routing Algorithms

Abstract

QoS routing plays a critical role in providing QoS support in the Internet. Most existing QoS routing algorithms employ the strategy of unidirectional search in route selection. Bidirectional search has been recognized as an effective strategy for fast route acquisition in identifying the shortest path connecting a pair of nodes. However, its efficiency has not been well established in the context of route selection subject to multiple additive constraints, which is in general NP-Complete. In this paper, we study how to employ bidirectional search to support efficient QoS routing subject to multiple additive constraints. The major contributions in this paper are as follows. First, we propose a <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex> </formula> shortest path algorithm using bidirectional search, whose complexity is deduced to be <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(\sqrt{k}\vert V \vert\lg (\vert V \vert) + k\vert E\vert)$</tex> </formula> , where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\vert V \vert$</tex> </formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\vert E \vert$</tex> </formula> represent the number of nodes and links in the network, respectively. Second, we show that bidirectional search can significantly accelerate the convergence of several existing QoS routing algorithms. Third, we propose a novel cost-effective bidirectional multi-constrained routing algorithm, which can greatly alleviate the forwarding state scalability issue by supporting stateless QoS routing in IP networks via IP tunneling or constraints-based alternate routing in MPLS networks via label stacks. It has the fastest known on-line running time <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(\vert V\vert)$</tex> </formula> . Theoretical and simulation results are given to demonstrate the high performance of our proposed algorithm in identifying QoS-satisfied paths and also in efficient resource utilization as compared with existing algorithms.