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Computing Steiner minimum trees in Hamming metric is a well studied problem that has applications in several fields of science such as computational linguistics and computational biology. Among all methods for finding such trees, algorithms using variations of a branch and bound method developed by Penny and Hendy have been the fastest for more than 20 years. In this paper we describe a new pruning approach that is superior to previous methods and its implementation. IntroductionWe are interested in computing a Steiner minimum tree in Hamming metric. Given a set T ⊆ U of required points (terminals) in an universe U and a cost function c : U × U → R, a Steiner tree is a tree connecting T ∪ S for a subset S ⊆ U . The elements of S are called the Steiner points. A Steiner minimum tree SMT(T ), is a Steiner tree of minimal cost.The Steiner tree problem is one of the most studied NP-hard optimization problems. In this paper we elaborate on the variant where U is the set of strings of size d over a finite alphabet Σ and where c is the Hamming distance between two strings, i.e. the number of characters in which two strings differ. As the general version this variant is known to be NP-hard too [6].One main application of the Steiner tree problem in Hamming metric is the computation of evolutionary trees in bioinformatics (in this context also called phylogenetic trees) and in computational linguistics. We elaborate on the use in bioinformatics.The problem in bioinformatics reads as follows: Given a set of species, we want to determine their ancestral relationship. In order to build the tree, we compare specific features of the species under the natural assumption that species with similar features are closely related. Building a tree implicitly makes the assumption that all species have evolved from a common ancestor and no recombination has occurred (which is generally not true). Classic phylogenetics dealt mainly

Hard real-time systems require tasks to finish in time. To guarantee the timeliness of such a system, static timing analyses derive upper bounds on the worst-case execution time (WCET) of tasks. There are two types of timing analyses: numeric and parametric. A numeric analysis derives a numeric timing bound and, to this end, assumes all information such as loop bounds to be given a priori. If these bounds are unknown during analysis time, a parametric analysis can compute a timing formula parametric in these variables. A performance bottleneck of timing analyses, numeric and especially parametric, is the so-called path analysis, which determines the path in the analyzed task with the longest execution time bound. In this paper, we present a new approach to path analysis. This approach exploits the often rather regular structure of software for hard real-time and safety-critical systems. As we show in the evaluation of this paper, we strongly improve upon former techniques in terms of precision and runtime in the parametric case. Even in the numeric case, the approach competes with state-of-the-art techniques and may be an alternative to commercial tools employed for path analysis.

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Abstract.A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem.This paper considers several problems of that kind; the first problem was studied before in [1,6] and aims to select and assign powers to k out of a total of n wireless network stations such that all stations are within reach of at least one of the selected stations. We show that the problem can be (1+ ) approximated by only looking at a small subset of the input,, i.e. independent of n and polynomial in k and 1/ . Here d denotes the dimension of the space where the wireless devices are distributed, so typically d ≤ 3 and α describes the relation between the Euclidean distance between two stations and the power consumption for establishing a wireless connection between them. Using this coreset we are able to improve considerably on the running time of n ((α/ ) O(d) ) for the algorithm by Bilo et al. at ESA'05 ([6]) actually obtaining a running time that is linear in n. Furthermore we sketch how outliers can be handled in our coreset construction. The second problem deals with the energy-efficient, bounded-hop multicast operation: Given a subset C out of a set of n stations and a designated source node s we want to assign powers to the stations such that every node in C is reached by a transmission from s within k hops. Again we show that a coreset of size independent of n and polynomial in k, |C|, 1/ exists, and use this to provide an algorithm which runs in time linear in n.The last problem deals with a variant of non-metric TSP problem where the edge costs are the squared Euclidean distances; this problem is motivated by data aggregation schemes in wireless sensor networks. We show that a good TSP tour under Euclidean edge costs can be very bad in the squared distance measure and provide a simple constant approximation algorithm, partly improving upon previous results in [5], [4].