Related papers: Geometric Freeze-Tag Problem
We give an $O(\log^2 n)$-query algorithm for finding a Tarski fixed point over the $4$-dimensional lattice $[n]^4$, matching the $\Omega(\log^2 n)$ lower bound of [EPRY20]. Additionally, our algorithm yields an ${O(\log^{\lceil…
The Calisson puzzle is a tiling puzzle in which one must tile a triangular grid inside a hexagon with lozenges, under the constraint that certain prescribed edges remain tile boundaries and that adjacent lozenges along these edges have…
Recent works have demonstrated great success in pre-training large-scale autoregressive language models on massive GPUs. To reduce the wall-clock training time, a common practice is to increase the batch size and learning rate. However,…
Selectively picking a target fruit surrounded by obstacles is one of the major challenges for fruit harvesting robots. Different from traditional obstacle avoidance methods, this paper presents an active obstacle separation strategy that…
Follow-the-leader (FTL) motion is essential for continuum robots operating in fragile and confined environments. It allows the robot to exert minimal force on its surroundings, reducing the risk of damage. This paper presents a novel design…
Given $r\geq2$ and an $r$-uniform hypergraph $F$, the $F$-bootstrap process starts with an $r$-uniform hypergraph $H$ and, in each time step, every hyperedge which "completes" a copy of $F$ is added to $H$. The maximum running time of this…
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems…
This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…
Task and motion planning (TAMP) algorithms aim to help robots achieve task-level goals, while maintaining motion-level feasibility. This paper focuses on TAMP domains that involve robot behaviors that take extended periods of time (e.g.,…
Real time applications such as robotic require real time actions based on the immediate available data. Machine learning and artificial intelligence rely on high volume of training informative data set to propose a comprehensive and useful…
Humanoid robots have the potential capability to perform a diverse range of manipulation tasks, but this is based on a robust and precise standing controller. Existing methods are either ill-suited to precisely control high-dimensional…
Motion planning trajectories for a multi-limbed robot to climb up walls requires a unique combination of constraints on torque, contact force, and posture. This paper focuses on motion planning for one particular setup wherein a six-legged…
We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
We give a new fpt algorithm testing isomorphism of $n$-vertex graphs of tree width $k$ in time $2^{k\operatorname{polylog} (k)}\operatorname{poly} (n)$, improving the fpt algorithm due to Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh (FOCS…
Over the last years collaborative robots have gained great success in manufacturing applications where human and robot work together in close proximity. However, current ISO/TS-15066-compliant implementations often limit the efficiency of…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred…
The structure of Markov equivalence classes (MECs) of causal DAGs has been studied extensively. A natural question in this regard is to algorithmically find the number of MECs with a given skeleton. Until recently, the known results for…
We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. Boolean-width is similar to rank-width, which is related to the number of $GF[2]$-sums (1+1=0) of…