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An st-shortest path, or st-path for short, in a graph G is a shortest (induced) path from s to t in G. Two st-paths are said to be adjacent if they differ on exactly one vertex. A reconfiguration sequence between two st-paths P and Q is a…

Computational Complexity · Computer Science 2024-06-19 Nicolas Bousquet , Kshitij Gajjar , Abhiruk Lahiri , Amer E. Mouawad

Snakes are a remarkable evolutionary success story. Many snake-inspired robots have been proposed over the years. Soft robotic snakes (SRS) with their continuous and smooth bending capability better mimic their biological counterparts'…

Robotics · Computer Science 2020-10-23 Dimuthu D. Arachchige , Yue Chen , Isuru S. Godage

We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space.…

Algebraic Topology · Mathematics 2007-05-23 Michael Farber , Serge Tabachnikov , Sergey Yuzvinsky

In the Token Jumping problem we are given a graph $G = (V,E)$ and two independent sets $S$ and $T$ of $G$, each of size $k \geq 1$. The goal is to determine whether there exists a sequence of $k$-sized independent sets in $G$, $\langle S_0,…

Computational Complexity · Computer Science 2025-01-15 Valentin Bartier , Nicolas Bousquet , Clément Dallard , Kyle Lomer , Amer E. Mouawad

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments like earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when…

Biological Physics · Physics 2025-09-22 Qiyuan Fu , Sean W. Gart , Thomas W. Mitchel , Jin Seob Kim , Gregory S. Chirikjian , Chen Li

We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and remove an edge from the other end. We…

Data Structures and Algorithms · Computer Science 2019-05-03 Erik D. Demaine , David Eppstein , Adam Hesterberg , Kshitij Jain , Anna Lubiw , Ryuhei Uehara , Yushi Uno

We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box…

Data Structures and Algorithms · Computer Science 2023-07-21 Michal Pilipczuk , Mathieu Mari , Timothe Picavet

In unlabeled multi-robot motion planning several interchangeable robots operate in a common workspace. The goal is to move the robots to a set of target positions such that each position will be occupied by some robot. In this paper, we…

Robotics · Computer Science 2015-04-21 Kiril Solovey , Dan Halperin

We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering…

Data Structures and Algorithms · Computer Science 2015-04-22 Dániel Marx , Michał Pilipczuk

In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots…

Computational Geometry · Computer Science 2020-04-28 Thomas Brocken , G. Wessel van der Heijden , Irina Kostitsyna , Lloyd E. Lo-Wong , Remco J. A. Surtel

Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using…

Robotics · Computer Science 2026-05-01 Liangting Wu , Roberto Tron

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Computational Complexity · Computer Science 2021-03-09 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

Graph Burning asks, given a graph $G = (V,E)$ and an integer $k$, whether there exists $(b_{0},\dots,b_{k-1}) \in V^{k}$ such that every vertex in $G$ has distance at most $i$ from some $b_{i}$. This problem is known to be NP-complete even…

Data Structures and Algorithms · Computer Science 2020-09-29 Yasuaki Kobayashi , Yota Otachi

We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents…

Data Structures and Algorithms · Computer Science 2015-03-20 Erik D. Demaine , MohammadTaghi Hajiaghayi , Dániel Marx

In this paper, the parking problem of a swarm of mobile robots has been studied. The robots are deployed at the nodes of an infinite grid, which has a subset of prefixed nodes marked as parking nodes. Each parking node p_i has a capacity of…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-10-17 Abhinav Chakraborty , Krishnendu Mukhopadhyaya

Unlabeled motion planning involves assigning a set of robots to target locations while ensuring collision avoidance, aiming to minimize the total distance traveled. The problem forms an essential building block for multi-robot systems in…

In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit…

Discrete Mathematics · Computer Science 2019-04-29 Dehia Ait-Ferhat , Vincent Juliard , Gautier Stauffer , Andres Torres

Traversing environments with arbitrary obstacles poses significant challenges for bipedal robots. In some cases, whole body motions may be necessary to maneuver around an obstacle, but most existing footstep planners can only select from a…

Robotics · Computer Science 2017-03-22 Michael X. Grey , Aaron D. Ames , C. Karen Liu

We study the Universal Solvability of Robot Motion Planning on Graphs (USolR) problem: given an undirected graph $G = (V, E)$ and $p$ robots, determine whether any arbitrary configuration of the robots can be transformed into any other…

Computational Complexity · Computer Science 2026-02-10 Anubhav Dhar , Pranav Nyati , Tanishq Prasad , Ashlesha Hota , Sudeshna Kolay

In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…

Data Structures and Algorithms · Computer Science 2024-06-03 N. R. Aravind , Roopam Saxena