Rouven Naujoks

Precise and efficient parametric path analysis

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.

Computing steiner minimum trees in Hamming metric

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.

Power assignment problems in wireless communication: Covering points by disks, reaching few receivers quickly, and energy-efficient travelling salesman tours

In this paper, we present approximation algorithms for a variety of problems occurring in the design of energy-efficient wireless communication networks. We first study the k-station network problem, where for a set S of stations and some constant k, one wants to assign transmission powers to at most k senders such that every station in S can receive a signal from at least one sender. We give a (1+@e)-approximation algorithm for this problem. The second problem deals with energy-efficient networks, allowing bounded hop multicast operations, that is given a subset C of the stations S and a designated source node s@?S, we want to assign powers to the sending stations, such that every node in C can be reached by a transmission from s within k hops. For this problem, we provide an algorithm which runs in time linear in |S|. The last problem deals with a variant of the non-metric TSP problem where the edge costs correspond to the Euclidean distances to the power of some @a>=1; this problem is motivated by data aggregation schemes in wireless sensor networks. We provide a simple constant approximation algorithm, which improves upon previous results when 2=<@a=<2.7.

A column generation approach to scheduling of periodic tasks

We present an algorithm based on column generation for a real time scheduling problem, in which all tasks appear regularly after a given period. Furthermore, the tasks exchange messages, which have to be transferred over a bus, if the tasks involved are executed on different ECUs. Experiments show that for large instances our preliminary implementation is faster than the previous approach based on an integer linear programming formulation using a state-of-the-art solver.

Minimum-energy broadcast with few senders

Broadcasting a message from a given source node to all other nodes is a fundamental task during the operation of a wireless network. In many application scenarios the network nodes have only a limited energy supply, hence minimizing the energy consumption of any communication task prolongs the lifetime of the network. During a broadcast operation using intermediate nodes to relay messages within the network might decrease the overall energy consumption since the cost of transmitting a message grows super-linearly with the distance. On the other hand using too many intermediate nodes during a broadcast operation increases both latency as well as the chances that some transmission could not properly received (e.g. due to interference). In this paper we consider a constrained broadcast operation, where a source node wants to send a message to all other nodes in the network but at most k nodes are allowed to participate actively, i.e. transmit the message. Restricting the number of transmitting nodes helps in reducing interference, latency and increasing reliability of the broadcast operation, of course at the cost of a slightly higher energy consumption. For the case of network nodes embedded in the Euclidean plane we provide a (1+Ɛ)- approximation algorithm which runs in time linear in n and polynomial in 1/Ɛ but with an exponential dependence on k. As an alternative we therefore also provide an O(1)-approximation whose running time is linear in n and polynomial in k. The existence of a (1 + Ɛ)-approximation algorithm is in stark contrast to the unconstrained broadcast problem where even in the Euclidean plane no algorithm with approximation factor better than 6 is known so far.

Reconstructing phylogenetic networks with one recombination

In this paper we propose a new method for reconstructing phylogenetic networks under the assumption that recombination events have occurred rarely. For a fixed number of recombinations, we give a generalization of the maximum parsimony criterion. Furthermore, we describe an exact algorithm for one recombination event and show that in this case our method is not only able to identify the recombined sequence but also to reliably reconstruct the complete evolutionary history.

On the low-dimensional steiner minimum tree problem in hamming metric

It is known that the d-dimensional Steiner Minimum Tree Problem in Hamming metric is NP-complete if d is considered to be a part of the input. On the other hand, it was an open question whether the problem is also NP-complete in fixed dimensions. In this paper we answer this question by showing that the problem is NP-complete for any dimension strictly greater than 2. We also show that the Steiner ratio is 2 - 2/d for d ≥ 2. Using this result, we tailor the analysis of the so-called k-LCA approximation algorithm and show improved approximation guarantees for the special cases d = 3 and d = 4.

Symbolic worst case execution times

In immediate or hard real-time systems the correctness of an operation depends not only upon its logical correctness, but also on the time in which it is computed. In such systems, it is imperative that operations are performed within a given deadline because missing this deadline constitutes the failure of the complete system. Such systems include medical systems, flight control systems and other systems whose failure in responding punctually results in a high economical loss or even in the loss of human lives. These systems are usually analyzed in a sequence of steps in which first, a socalled control flow graph (CFG) is constructed that represents possible program flows. Furthermore, bounds on the time necessary to execute small code blocks are computed along with bounds on the number of possible executions of the program loops. Depending on the type of the analysis, these loop bounds can either be numerical values or symbolic variables, corresponding to inputs given for instance by a user or by sensors. In the last step, in such a CFG the weight of a longest path with respect to the loop bounds is computed, reflecting a bound on the worst case execution time. In this paper, we will show how to compute such symbolic longest path weights in CFGs of software with a rather regular structure like software developed for hard real-time systems. We will present the first algorithm that is capable of computing such paths in time polynomial in the size of both the input and the output. Our approach replaces the application of integer linear programming solvers in the case of purely numerical loop bounds. Furthermore, it improves upon the speed and accuracy of existing approaches in the case of symbolic bounds.