An Optimal Competitive Strategy for Walking in Streets

The complexity of shortest path and dilation bounded interval routing

The minimum broadcast range assignment problem on linear multi-hop wireless networks

Deterministic monotone algorithms for scheduling on related machines

We investigate the power of counting in Group Isomorphism. We first leverage the count-free variant of the Weisfeiler–Leman Version I algorithm for groups [J. Brachter and P. Schweitzer, On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786] in tandem with bounded non-determinism and limited counting to improve the parallel complexity of isomorphism testing for several families of groups. These families include: • Direct products of non-Abelian simple groups. • Coprime extensions, where the normal Hall subgroup is Abelian and the complement is an [Formula: see text]-generated solvable group with solvability class [Formula: see text]. This notably includes instances where the complement is an [Formula: see text]-generated nilpotent group. This problem was previously known to be in [Formula: see text] [Y. Qiao, J. M. N. Sarma and B. Tang, On isomorphism testing of groups with normal Hall subgroups, in Proc. 28th Symp. Theoretical Aspects of Computer Science, Dagstuhl Castle, Leibniz Center for Informatics, 2011), pp. 567–578, doi:10.4230/LIPIcs. STACS.2011.567], and the complexity was recently improved to [Formula: see text] [J. A. Grochow and M. Levet, On the parallel complexity of group isomorphism via Weisfeiler–Leman, in 24th Int. Symp. Fundamentals of Computation Theory, eds. H. Fernau and K. Jansen, Lecture Notes in Computer Science, Vol. 14292, September 18–21, 2023, Trier, Germany (Springer, 2023), pp. 234–247]. • Graphical groups of class 2 and exponent [Formula: see text] [A. H. Mekler, Stability of nilpotent groups of class 2 and prime exponent, J. Symb. Logic 46(4) (1981) 781–788] arising from the CFI and twisted CFI graphs [J.-Y. Cai, M. Fürer and N. Immerman, An optimal lower bound on the number of variables for graph identification, Combinatorica 12(4) (1992) 389–410], respectively. In particular, our work improves upon previous results of Brachter and Schweitzer [On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786]. Notably, each of these families was previously known to be identified by the counting variant of the more powerful Weisfeiler–Leman Version II algorithm. We finally show that the q-ary count-free pebble game is unable to even distinguish Abelian groups. This extends the result of Grochow and Levet (ibid), who established the result in the case of [Formula: see text]. The general theme is that some counting appears necessary to place [Formula: see text] into [Formula: see text].

Selfish unsplittable flows

This special issue contains nine articles which are based on extended abstracts that were presented at the 28th Symposium on Theoretical Aspects of Computer Science (STACS), which was held at Technische Universitat Dortmund, Germany, March 10– 12, 2011. These extended abstracts were among the top papers of those that were chosen for presentation at STACS 2011 in a highly competitive peer-review process (after which only 54 papers out of 271 submission were accepted). Compared with the original extended abstracts the articles have been strongly revised and extended by full proofs and additional results. They underwent a further rigorous reviewing process, following the TOCS standard, completely independent from the selection process of STACS 2011. Three articles are about formal languages. The first two investigate size issues for automata and (extended) regular expressions, respectively, while the third one investigates the syntactic monoids of regular languages over infinite alphabets. The article Series Parallel Digraphs with Loops by Stefan Gulan studies the question which kinds of finite automata can be translated into regular expressions of linear size. It gives a very comprehensive answer to this question by showing that such linear translations are possible from automata with a certain underlying graph structure, series parallel loop graphs, into regular expressions and vice versa. Furthermore it characterizes this graph class (within the class of hammocks, i.e., all graphs with dis-

In the last years, kernelization with structural parameters has been an active area of research within the field of parameterized complexity. As a relevant example, Gajarský et al. (J Comput Syst Sci 84:219–242, 2017) proved that every graph problem satisfying a property called finite integer index admits a linear kernel on graphs of bounded expansion and an almost linear kernel on nowhere dense graphs, parameterized by the size of a c-treedepth modulator, which is a vertex set whose removal results in a graph of treedepth at most c, where $$c \ge 1$$ is a fixed integer. The authors left as further research to investigate this parameter on general graphs, and in particular to find problems that, while admitting polynomial kernels on sparse graphs, behave differently on general graphs. In this article we answer this question by finding two very natural such problems: we prove that Vertex Cover admits a polynomial kernel on general graphs for any integer $$c \ge 1$$ , and that Dominating Set does not for any integer $$c \ge 2$$ even on degenerate graphs, unless $$\text {NP} \subseteq \text {coNP}/\text {poly}$$ . For the positive result, we build on the techniques of Jansen and Bodlaender (Proceedings of the 28th symposium on theoretical aspects of computer science (STACS), volume 9 of LIPIcs, pp 177–188, 2011), and for the negative result we use a polynomial parameter transformation for $$c\ge 3$$ and an or-cross-composition for $$c = 2$$ . As existing results imply that Dominating Set admits a polynomial kernel on degenerate graphs for $$c = 1$$ , our result provides a dichotomy about the existence of polynomial kernels for Dominating Set on degenerate graphs with this parameter.

We consider distributed deterministic broadcasting in synchronous radio networks. A node receives a message in a given round if and only if exactly one of its neighbors transmits. The source message has to reach all nodes. We assume that nodes do not know the network topology or even their immediate neighborhood. (Such networks are called ad hoc.) We are concerned with two efficiency measures of broadcasting algorithms: their execution time (number of rounds) and their cost (number of transmissions). We focus our study on the execution time of algorithms which have cost close to minimum. We consider two scenarios depending on whether nodes know or do not know global parameters of the network: the number n of nodes and the eccentricity D of the source. Our main contribution is proving tight lower bounds on the time of low-cost broadcasting which show sharp differences between these scenarios. In each case, we also give broadcasting algorithms whose performance matches these lower bounds. © 2002 Wiley Periodicals, Inc.

We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke [Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science, 2008, pp. 669–680] by devising a deterministic approach whose performance guarantee is . In addition, we study preemptive online algorithms, a class of algorithms related to one-pass semi-streaming algorithms, where we are allowed to maintain only a feasible matching in memory at any point in time. We provide a lower bound of 4.967 on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges that is not necessarily a feasible matching. We conclude by presenting an empirical study, conducted in order to compare the practical performance of our approach to that of previously suggested algorithms.

The Symposium on Theoretical Aspects of Computer Science (STACS) is held annually, alternating between France and Germany, and has become one of the most important European annual meetings for the theoretical computer science community covering a wide range of topics in the area of foundations of computer science: algorithms and data structures, automata and formal languages, computational and structural complexity, logic, verification, and current challenges. The 24th conference of the series, STACS 2007, was held at the University of Aachen on February 22–24. Its call for papers led to approximately 450 submissions from all over the world. The scientific quality of the submissions made selecting the best ones a very difficult task. During the two-day, very intense meeting of the Program Committee, 54 papers (only 12% of the submissions) could be chosen for presentation at the conference. Due to this highly selective process, many good and relevant papers with positive reviews could not be included in the final program. On the other hand such a rigorous selection process, which is usual for STACS, is the guarantee that this conference series is a scientifically rich and very fruitful forum for theoretical computer science. The articles in this special issue of Theory of Computing Systems are a further selection from the best results presented at STACS 2007. The full versions of these papers underwent an additional strict refereeing process as is standard for a high-level scientific journal. The contributions illustrate very well the wide range of STACS. We express our gratitude to all authors for their contributions and to the referees for their helpful reports. We also thank Alan Selman for the smooth cooperation.

Distance Labeling for Permutation Graphs

STACS '93 : 10th Symposium on Theoretical Aspects of Computer Science '93, February 25–27, 1993

Characterizing LR-visibility polygons and related problems

This paper studies a searching problem in an unknown street. A simple polygon [Formula: see text] with two distinguished vertices, [Formula: see text] and [Formula: see text], is called a street if the two boundary chains from [Formula: see text] to [Formula: see text] are mutually weakly visible. We use a mobile robot to locate [Formula: see text] starting from [Formula: see text]. Assume that the robot has a limited sensing capability that can only detect the constructed edges (also called gaps) on the boundary of its visible region, but cannot measure any angle or distance. The robot does not have knowledge of the street in advance. We present a new competitive strategy for this problem and prove that the length of the path generated by the robot is at most 9-times longer than the shortest path. We also propose a matching lower bound to show that our strategy is optimal. Compared with the previous strategy, we further relaxed the restriction that the robot should take a marking device and use the data structure S-GNT. The analysis of our strategy is tight.

Contributors