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We present an algorithm that computes a shortest non-contractible and a shortest non-separating cycle on an orientable combinatorial surface of bounded genus in O(n \log n) time, where n denotes the complexity of the surface. This solves a…

Computational Geometry · Computer Science 2007-05-23 Martin Kutz

In the field of swarm robotics, one of the most studied problem is Gathering. It asks for a distributed algorithm that brings the robots to a common location, not known in advance. We consider the case of robots constrained to move along…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-12 Serafino Cicerone , Alessia Di Fonso , Gabriele Di Stefano , Alfredo Navarra

We consider the problem of collective exploration of a known $n$-node edge-weighted graph by $k$ mobile agents that have limited energy but are capable of energy transfers. The agents are initially placed at an arbitrary subset of nodes in…

Discrete Mathematics · Computer Science 2021-02-26 J. Czyzowicz , S. Dobrev , R. Killick , E. Kranakis , D. Krizanc , L. Narayanan , J. Opatrny , D. Pankratov , S. Shende

This paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-08-08 Marjorie Bournat , Ajoy K. Datta , Swan Dubois

We consider the problem of organizing a scattered group of $n$ robots in two-dimensional space, with geometric maximum distance $D$ between robots. The communication graph of the swarm is connected, but there is no central authority for…

Robotics · Computer Science 2015-05-13 Dominik Krupke , Michael Hemmer , James McLurkin , Yu Zhou , Sandor P. Fekete

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-12 Giuseppe Antonio Di Luna , Paola Flocchini , Linda Pagli , Giuseppe Prencipe , Nicola Santoro , Giovanni Viglietta

We resolve the space complexity of single-pass streaming algorithms for approximating the classic set cover problem. For finding an $\alpha$-approximate set cover (for any $\alpha= o(\sqrt{n})$) using a single-pass streaming algorithm, we…

Data Structures and Algorithms · Computer Science 2016-03-21 Sepehr Assadi , Sanjeev Khanna , Yang Li

In order to investigate the routing aspects of small-world networks, Kleinberg proposes a network model based on a $d$-dimensional lattice with long-range links chosen at random according to the $d$-harmonic distribution. Kleinberg shows…

Discrete Mathematics · Computer Science 2007-05-23 Jianyang Zeng , Wen-Jing Hsu , Jiangdian Wang

We introduce and study the Joint Task Assistance Planning problem which generalizes prior work on optimizing assistance in robotic collaboration. In this setting, two robots operate over predefined roadmaps, each represented as a graph…

Robotics · Computer Science 2026-02-25 Omer Daube , Oren Salzman

In this paper, we tackle the problem of planning an optimal coverage path for a robot operating indoors. Many existing approaches attempt to discourage turns in the path by covering the environment along the least number of coverage lines,…

Robotics · Computer Science 2022-05-30 Megnath Ramesh , Frank Imeson , Baris Fidan , Stephen L. Smith

We consider exploration of finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules. The number of possible shapes of a metamorphic robotic system grows as the number of modules increases. The shape of…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-05 Keisuke Doi , Yukiko Yamauchi , Shuji Kijima , Masafumi Yamashita

Future applications in environmental monitoring, delivery of services and transportation of goods motivate the study of deployment and partitioning tasks for groups of autonomous mobile agents. These tasks are achieved by recent coverage…

Optimization and Control · Mathematics 2009-12-28 Francesco Bullo , Ruggero Carli , Paolo Frasca

Building structures can allow a robot to surmount large obstacles, expanding the set of areas it can reach. This paper presents a planning algorithm to automatically determine what structures a construction-capable robot must build in order…

Robotics · Computer Science 2018-12-12 Tarik Tosun , Cynthia Sung , Colin McCloskey , Mark Yim

In this paper, we present a communication-free algorithm for distributed coverage of an arbitrary network by a group of mobile agents with local sensing capabilities. The network is represented as a graph, and the agents are arbitrarily…

Systems and Control · Computer Science 2016-02-01 A. Yasin Yazicioglu , Magnus Egerstedt , Jeff S. Shamma

Given a set of $n$ point robots inside a simple polygon $P$, the task is to move the robots from their starting positions to their target positions along their shortest paths, while the mutual visibility of these robots is preserved.…

Computational Geometry · Computer Science 2025-09-09 Rusul J. Alsaedi , Joachim Gudmundsson , André van Renssen

We present a biologically inspired design for swarm foraging based on ant's pheromone deployment, where the swarm is assumed to have very restricted capabilities. The robots do not require global or relative position measurements and the…

Robotics · Computer Science 2021-09-10 Steven Adams , Daniel Jarne Ornia , Manuel Mazo

Using elementary distributed computing techniques we suggest an explanation for two unexplained phenomena in regards to ant colonies, (a) a substantial amount of ants in an ant colony are idle, and (b) the observed low survivability of new…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-05-23 Yehuda Afek , Deborah M. Gordon , Moshe Sulamy

We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to…

Machine Learning · Computer Science 2023-09-18 Lukas Taus , Yen-Hsi Richard Tsai

The exploration problem in the discrete universe, using identical oblivious asynchronous robots without direct communication, has been well investigated. These robots have sensors that allow them to see their environment and move…

Multiagent Systems · Computer Science 2012-05-23 Ajoy K. Datta , Anissa Lamani , Lawrence L. Larmore , Franck Petit

When considering motion planning for a swarm of $n$ labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel, collision-free robot motions. The objective is to reach the…

Computational Geometry · Computer Science 2024-07-25 Sándor P. Fekete , Peter Kramer , Christian Rieck , Christian Scheffer , Arne Schmidt