Polynomial Time Approximation Algorithms for Multi-Constrained QoS Routing

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We study the multi-constrained quality-of-service (QoS) routing problem where one seeks to find a path from a source to a destination in the presence of <formula formulatype="inline"><tex>$K\geq 2$</tex></formula> additive end-to-end QoS constraints. This problem is NP-hard and is commonly modeled using a graph with <formula formulatype="inline"><tex>$n$</tex></formula> vertices and <formula formulatype="inline"><tex>$m$</tex></formula> edges with <formula formulatype="inline"> <tex>$K$</tex></formula> additive QoS parameters associated with each edge. For the case of <formula formulatype="inline"><tex>$K=2$</tex></formula>, the problem has been well studied, with several provably good polynomial time-approximation algorithms reported in the literature, which enforce one constraint while approximating the other. We first focus on an optimization version of the problem where we enforce the first constraint and approximate the other <formula formulatype="inline"><tex>$K-1$</tex></formula> constraints. We present an <formula formulatype="inline"><tex>$O(mn\log\log\log n+mn/\epsilon)$</tex></formula> time <formula formulatype="inline"><tex>$(1+\epsilon)(K-1)$</tex></formula>-approximation algorithm and an <formula formulatype="inline"><tex>$O(mn\log\log\log n+m(n/\epsilon)^{K-1})$</tex> </formula> time <formula formulatype="inline"><tex>$(1+\epsilon)$</tex></formula>-approximation algorithm, for any <formula formulatype="inline"><tex>$\epsilon&gt;0$</tex></formula>. When <formula formulatype="inline"><tex>$K$</tex></formula> is reduced to 2, both algorithms produce an <formula formulatype="inline"><tex>$(1+\epsilon)$</tex> </formula>-approximation with a time complexity better than that of the best-known algorithm designed for this special case. We then study the decision version of the problem and present an <formula formulatype="inline"><tex>$O(m(n/\epsilon)^{K-1})$</tex> </formula> time algorithm which either finds a feasible solution or confirms that there does </para>