@article{66838, abstract = {{The sliding square model is a widely used abstraction for studying self-reconfigurable robotic systems, where modules are square-shaped robots that move by sliding or rotating over one another. In this paper, we propose a novel distributed algorithm that enables a group of modules to reconfigure into a rhombus shape, starting from an arbitrary side-connected configuration. It is connectivity-preserving and operates under minimal assumptions: one leader module, common chirality, constant memory per module, and visibility and communication restricted to immediate neighbors. Unlike prior work, which relaxes the original sliding square move-set, our approach uses the unmodified move-set, addressing the additional challenge of handling locked configurations. Our algorithm is sequential in nature and operates with a worst-case time complexity of O(n^2) rounds, which is optimal for sequential algorithms. To improve runtime, we introduce two parallel variants of the algorithm. Both rely on a spanning tree data structure, allowing modules to make decisions based on local connectivity. Our experimental results show a significant speedup for the first variant, and a linear average runtime for the second variant, which is worst-case optimal for parallel algorithms.}}, author = {{Kostitsyna, Irina and Liedtke, David and Scheideler, Christian}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{modular robots, distributed algorithms, sliding squares}}, publisher = {{Elsevier BV}}, title = {{{Distributed rhombus formation of sliding squares}}}, doi = {{10.1016/j.tcs.2026.116196}}, volume = {{1085}}, year = {{2026}}, } @article{62051, author = {{Hinnenthal, Kristian and Liedtke, David Jan and Scheideler, Christian}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, publisher = {{Elsevier BV}}, title = {{{Efficient shape formation by 3D hybrid programmable matter: An algorithm for low diameter intermediate structures}}}, doi = {{10.1016/j.tcs.2025.115552}}, volume = {{1057}}, year = {{2025}}, } @article{61172, author = {{Coy, Sam and Czumaj, Artur and Scheideler, Christian and Schneider, Philipp and Werthmann, Julian}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, publisher = {{Elsevier BV}}, title = {{{Routing Schemes for Hybrid Communication Networks}}}, doi = {{10.1016/j.tcs.2023.114352}}, volume = {{985}}, year = {{2024}}, } @article{48871, abstract = {{Most runtime analyses of randomised search heuristics focus on the expected number of function evaluations to find a unique global optimum. We ask a fundamental question: if additional search points are declared optimal, or declared as desirable target points, do these additional optima speed up evolutionary algorithms? More formally, we analyse the expected hitting time of a target set OPT{$\cup$}S where S is a set of non-optimal search points and OPT is the set of optima and compare it to the expected hitting time of OPT. We show that the answer to our question depends on the number and placement of search points in S. For all black-box algorithms and all fitness functions with polynomial expected optimisation times we show that, if additional optima are placed randomly, even an exponential number of optima has a negligible effect on the expected optimisation time. Considering Hamming balls around all global optima gives an easier target for some algorithms and functions and can shift the phase transition with respect to offspring population sizes in the (1,{$\lambda$}) EA on OneMax. However, for the one-dimensional Ising model the time to reach Hamming balls of radius (1/2-{$ϵ$})n around optima does not reduce the asymptotic expected optimisation time in the worst case. Finally, on functions where search trajectories typically join in a single search point, turning one search point into an optimum drastically reduces the expected optimisation time.}}, author = {{Bossek, Jakob and Sudholt, Dirk}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{Evolutionary algorithms, pseudo-Boolean functions, runtime analysis}}, pages = {{113757}}, title = {{{Do Additional Target Points Speed Up Evolutionary Algorithms?}}}, doi = {{10.1016/j.tcs.2023.113757}}, year = {{2023}}, } @article{46310, abstract = {{Classic automated algorithm selection (AS) for (combinatorial) optimization problems heavily relies on so-called instance features, i.e., numerical characteristics of the problem at hand ideally extracted with computationally low-demanding routines. For the traveling salesperson problem (TSP) a plethora of features have been suggested. Most of these features are, if at all, only normalized imprecisely raising the issue of feature values being strongly affected by the instance size. Such artifacts may have detrimental effects on algorithm selection models. We propose a normalization for two feature groups which stood out in multiple AS studies on the TSP: (a) features based on a minimum spanning tree (MST) and (b) nearest neighbor relationships of the input instance. To this end we theoretically derive minimum and maximum values for properties of MSTs and k-nearest neighbor graphs (NNG) of Euclidean graphs. We analyze the differences in feature space between normalized versions of these features and their unnormalized counterparts. Our empirical investigations on various TSP benchmark sets point out that the feature scaling succeeds in eliminating the effect of the instance size. A proof-of-concept AS-study shows promising results: models trained with normalized features tend to outperform those trained with the respective vanilla features.}}, author = {{Heins, Jonathan and Bossek, Jakob and Pohl, Janina and Seiler, Moritz and Trautmann, Heike and Kerschke, Pascal}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{Feature normalization, Algorithm selection, Traveling salesperson problem}}, pages = {{123--145}}, title = {{{A study on the effects of normalized TSP features for automated algorithm selection}}}, doi = {{https://doi.org/10.1016/j.tcs.2022.10.019}}, volume = {{940}}, year = {{2023}}, } @article{33947, author = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{General Computer Science, Theoretical Computer Science}}, pages = {{261--291}}, publisher = {{Elsevier BV}}, title = {{{Gathering a Euclidean Closed Chain of Robots in Linear Time and Improved Algorithms for Chain-Formation}}}, doi = {{10.1016/j.tcs.2022.10.031}}, volume = {{939}}, year = {{2023}}, } @article{22510, abstract = {{Over the past decades, the Gathering problem, which asks to gather a group of robots in finite time given some restrictions, has been intensively studied. In this paper, we are given a group of n autonomous, dimensionless, deterministic, and anonymous robots, with bounded viewing range. Assuming a continuous time model, the goal is to gather these robots into one point in finite time. We introduce a simple convergence criterion that defines a new class of algorithms which perform gathering in O(nd) time, where d is the diameter of the initial robot configuration. We show that some gathering algorithms in the literature belong to this class and propose two new algorithms that belong to this class and have quadratic running time, namely, Go-To-The-Relative-Center algorithm (GTRC) and Safe-Go-To-The-Relative-Center algorithm (S-GTRC). We prove that the latter can perform gathering without collision by using a slightly more complex robot model: non oblivious, chiral, and luminous (i.e. robots have observable external memory, as in [8]). We also consider a variant of the Gathering problem, the Near-Gathering problem, in which robots must get close to each other without colliding. We show that S-GTRC solves the Near-Gathering problem in quadratic time and assumes a weaker robot model than the one assumed in the current state-of-the-art.}}, author = {{Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{Local algorithms, Distributed algorithms, Collisionless gathering, Mobile robots, Multiagent system}}, pages = {{41--60}}, title = {{{A continuous strategy for collisionless gathering}}}, doi = {{10.1016/j.tcs.2020.10.037}}, volume = {{852}}, year = {{2021}}, } @article{22511, abstract = {{In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile robots with limited viewing range in the plane. Remarquably, this algorithm exploits the fact that during its execution, many collisions of robots occur. Such collisions are interpreted as a success because it is assumed that such collided robots behave the same from now on. This is acceptable under the assumption that each robot is represented by a single point. Otherwise, collisions should be avoided. In this paper, we consider a continuous Go-To-The-Center algorithm in which the robots continuously observe the positions of their neighbors and adapt their speed (assuming a speed limit) and direction. Our first results are time bounds of O(n2) for gathering in two dimensions Euclidean space, and Θ(n) for the one dimension. Our main contribution is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center considering only the neighbors of a robot with respect to the Gabriel subgraph of the visibility graph, i.e. Go-To-The-Gabriel-Center algorithm. We show that this modification still correctly executes gathering in one and two dimensions, with the same time bounds as above. Simulations exhibit a severe difference of the behavior of the Go-To-The-Center and the Go-To-The-Gabriel-Center algorithms: Whereas lots of collisions occur during a run of the Go-To-The-Center algorithm, typically only one, namely the final collision occurs during a run of the Go-To-The-Gabriel-Center algorithm. We can prove this “collisionless property” of the Go-To-The-Gabriel-Center algorithm for one dimension. In two-dimensional Euclidean space, we conjecture that the “collisionless property” holds for almost every initial configuration. We support our conjecture with measurements obtained from the simulation where robots execute both continuous Go-To-The-Center and Go-To-The-Gabriel-Center algorithms. }}, author = {{Li, Shouwei and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{Local algorithms, Distributed algorithms, Collisionless gathering, Mobile robots, Multiagent system}}, pages = {{29--40}}, title = {{{The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots}}}, doi = {{10.1016/j.tcs.2020.11.009}}, volume = {{852}}, year = {{2021}}, } @article{16299, author = {{Castenow, Jannik and Fischer, Matthias and Harbig, Jonas and Jung, Daniel and Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{289--309}}, title = {{{Gathering Anonymous, Oblivious Robots on a Grid}}}, doi = {{10.1016/j.tcs.2020.02.018}}, volume = {{815}}, year = {{2020}}, } @article{2916, author = {{Brauer, Sascha}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{88--106}}, publisher = {{Elsevier}}, title = {{{Complexity of single-swap heuristics for metric facility location and related problems}}}, doi = {{10.1016/j.tcs.2018.04.048}}, volume = {{754}}, year = {{2019}}, } @article{16429, author = {{Kutyłowski, Jarosław and Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{3391--3405}}, title = {{{Optimal strategies for maintaining a chain of relays between an explorer and a base camp}}}, doi = {{10.1016/j.tcs.2008.04.010}}, year = {{2009}}, } @article{2999, author = {{Blömer, Johannes and Naewe, Stefanie}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{Geometry of numbers, Lattices, Shortest vectors}}, number = {{18}}, pages = {{1648 -- 1665}}, title = {{{Sampling methods for shortest vectors, closest vectors and successive minima}}}, doi = {{10.1016/j.tcs.2008.12.045}}, volume = {{410}}, year = {{2009}}, } @article{18790, author = {{Czumaj, Artur and Sohler, Christian}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, number = {{1}}, pages = {{37--52}}, title = {{{Testing hypergraph colorability}}}, doi = {{10.1016/j.tcs.2004.09.031}}, volume = {{331}}, year = {{2005}}, } @article{15058, author = {{Ziegler, Martin}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{14--26}}, title = {{{Stability versus speed in a computable algebraic model}}}, doi = {{10.1016/j.tcs.2005.09.053}}, year = {{2005}}, } @article{16521, author = {{Bezrukov, S. and Elsässer, R. and Monien, B. and Preis, R. and Tillich, J.-P.}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{155--174}}, title = {{{New spectral lower bounds on the bisection width of graphs}}}, doi = {{10.1016/j.tcs.2004.03.059}}, year = {{2004}}, } @article{16503, author = {{Meyer auf der Heide, Friedhelm and Schröder, Klaus and Schwarze, Frank}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{181--200}}, title = {{{Routing on networks of optical crossbars}}}, doi = {{10.1016/s0304-3975(97)86791-6}}, volume = {{196}}, year = {{1998}}, } @article{16504, author = {{Bäumker, Armin and Dittrich, Wolfgang and Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{175--203}}, title = {{{Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model}}}, doi = {{10.1016/s0304-3975(98)00020-6}}, year = {{1998}}, } @article{19818, author = {{Kleine Büning, Hans and Lettmann, Theodor and Mayr, Ernst W.}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{343--350}}, title = {{{Projections of vector addition system reachability sets are semilinear}}}, doi = {{10.1016/0304-3975(89)90055-8}}, year = {{1989}}, } @article{16765, author = {{Borodin, Allan and Fich, Faith E. and Meyer auf der Heide, Friedhelm and Upfal, Eli and Wigderson, Avi}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{57--68}}, title = {{{A tradeoff between search and update time for the implicit dictionary problem}}}, doi = {{10.1016/0304-3975(88)90018-7}}, year = {{1988}}, } @article{16781, author = {{Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{325--330}}, title = {{{Simulating probabilistic by deterministic algebraic computation trees}}}, doi = {{10.1016/0304-3975(85)90079-9}}, year = {{1985}}, }