Gathering a Euclidean Closed Chain of Robots in Linear Time and Improved Algorithms for Chain-Formation - Castenow, Jannik; Harbig, Jonas; Jung, Daniel; Knollmann, Till; Meyer auf der Heide, Friedhelm (Theoretical Computer Science)
Keywords: General Computer Science; Theoretical Computer Science

Do Additional Target Points Speed Up Evolutionary Algorithms? - Bossek, Jakob; Sudholt, Dirk (Theoretical Computer Science)
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,{$λ$}) 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.
Keywords: Evolutionary algorithms; pseudo-Boolean functions; runtime analysis

A study on the effects of normalized TSP features for automated algorithm selection - Heins, Jonathan; Bossek, Jakob; Pohl, Janina; Seiler, Moritz; Trautmann, Heike; Kerschke, Pascal (Theoretical Computer Science)
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.
Keywords: Feature normalization; Algorithm selection; Traveling salesperson problem

A continuous strategy for collisionless gathering - Li, Shouwei; Markarian, Christine; Meyer auf der Heide, Friedhelm; Podlipyan, Pavel (Theoretical Computer Science)
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.
Keywords: Local algorithms; Distributed algorithms; Collisionless gathering; Mobile robots; Multiagent system

The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots - Li, Shouwei; Meyer auf der Heide, Friedhelm; Podlipyan, Pavel (Theoretical Computer Science)
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.
Keywords: Local algorithms; Distributed algorithms; Collisionless gathering; Mobile robots; Multiagent system

Gathering Anonymous, Oblivious Robots on a Grid - Castenow, Jannik; Fischer, Matthias; Harbig, Jonas; Jung, Daniel; Meyer auf der Heide, Friedhelm (Theoretical Computer Science)

Complexity of single-swap heuristics for metric facility location and related problems - Brauer, Sascha (Theoretical Computer Science)

Sampling methods for shortest vectors, closest vectors and successive minima - Blömer, Johannes; Naewe, Stefanie (Theoretical Computer Science)
Keywords: Geometry of numbers; Lattices; Shortest vectors

Optimal strategies for maintaining a chain of relays between an explorer and a base camp - Kutyłowski, Jarosław; Meyer auf der Heide, Friedhelm (Theoretical Computer Science)

Testing hypergraph colorability - Czumaj, Artur; Sohler, Christian (Theoretical Computer Science)