An Improved Approximation Algorithm for the Uniform Cost-Distance Steiner Tree Problem
Conference: Workshop on Approximation and Online Algorithms 2020
Speaker: Ardalan Khazraei
Abstract: The cost-distance Steiner tree problem asks for a Steiner tree in a graph that minimizes the total cost plus a weighted sum of path delays from the root to the sinks. We present an improved approximation for the uniform cost-distance Steiner tree problem, where the delay of a path corresponds to the sum of edge costs along that path. Previous approaches deploy a bicriteria approximation algorithm for the length-bounded variant that does not take the actual delay weights into account. Our algorithm modifies a similar algorithm for the single-sink buy-at-bulk problem by Guha et al. [2009], allowing a better approximation factor for our problem. In contrast to the bicriteria algorithms it considers delay weights explicitly. Thereby, we achieve an approximation factor of (1+ \(\beta\) ), where \(\beta\) is the approximation factor for the Steiner tree problem. This improves the previously best known approximation factor for the uniform cost-distance Steiner tree problem from 2:87 to 2:39. This algorithm can be extended to the problem where the ratio of edge costs to edge delays throughout the graph is bounded from above and below. In particular, this shows that a previous inapproximability result (Chuzhoy et al. [2008]) requires large variations between edge delays and costs. Finally, we present an important application of our new algorithm in chip design. The cost-distance Steiner tree problem occurs as a Lagrangean subproblem when optimizing millions of Steiner trees with mutually depending path length bounds. We show how to quickly approximate a continuous relaxation of this problem with our new algorithm.
This is joined work with Stephan Held.