2nd Colloquium of Research Area KL

Date: July 12, 2013
Venue:  Seminar room 1st floor, Arithmeum, Lennéstr. 2, Bonn


15:45 Coffee and Tee (Lounge 2nd floor, Arithmeum, Lennéstr. 2)
16:15 Heiko Röglin: Smoothed Analysis of the Successive Shortest Path Algorithm
17:00 Coffee break
17:30 Stephan Held: Shallow Light Steiner Arborescences
  After the Colloquium there will be the opportunity to have dinner together



Heiko Röglin: Smoothed Analysis of the Successive Shortest Path Algorithm

The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that both the problem and the algorithms are well understood. However, some of the algorithms' running times observed in empirical studies contrast the running times obtained by worst-case analysis not only in the order of magnitude but also in the ranking when compared to each other. For example, the Successive Shortest Path (SSP) algorithm, which has an exponential worst-case running time, seems to outperform the strongly polynomial Minimum-Mean Cycle Canceling algorithm. To explain this discrepancy, we study the SSP algorithm in the framework of smoothed analysis and establish a bound of O(mn\phi‑(m + n log n)) for its smoothed running time. This shows that worst-case instances for the SSP algorithm are not robust and unlikely to be encountered in practice. (joint work with Tobias Brunsch, Kamiel Cornelissen, and Bodo Manthey)


Stephan Held: Shallow Light Steiner Arborescences

We consider the problem of constructing a Steiner arborescence broadcasting a signal from a root r to a set T of sinks in a metric space. The arborescence must obey delay bounds for each r-t-path (t in T), where the path delay is imposed by its total edge length and its inner vertices. We want to minimize the total length. Computing such arborescences is a central step in VLSI design where the problem is known as the repeater tree problem. Here it is used to compute topologies for repeater trees as well as symmetric fan-in trees, e.g. to layout parity bit functions.

We prove that there is no constant factor approximation algorithm unless P=NP and develop a bicriteria approximation algorithm trading off signal speed (shallowness) and total length (lightness). The latter generalizes results of Khuller et al., and Elkin and Solomon who do not consider vertex delays. Finally, we demonstrate that the new algorithm improves existing algorithms on real world VLSI instances. This is joint work with Daniel Rotter.