相关论文: Guarding Polygons with Holes

Let $S$ be a set of $n$ points in the plane. We present several different algorithms for finding a pair of points in $S$ such that any disk that contains that pair must contain at least $cn$ points of $S$, for some constant $c>0$. The first…

Given a polygon $H$ in the plane, the art gallery problem calls for fining the smallest set of points in $H$ from which every other point in $H$ is seen. We give a deterministic algorithm that, given any polygon $H$ with $h$ holes, $n$…

In the recently introduced model of fair partitioning of friends, there is a set of agents located on the vertices of an underlying graph that indicates the friendships between the agents. The task is to partition the graph into $k$…

In this paper, we consider the 1.5-dimensional orthogonal terrain guarding problem. In this problem, we assign an x-monotone chain T because each edge is either horizontal or vertical, and determine the minimal number of vertex guards for…

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the…

Patrolling consists of scheduling perpetual movements of a collection of mobile robots, so that each point of the environment is regularly revisited by any robot in the collection. In previous research, it was assumed that all points of the…

In the convex covering problem, we are given a convex polygon with holes $P$ and the goal is to cover $P$ using a small number of convex polygons that lie inside $P$. In this paper, we solve the problem using the following strategy. We find…

The well-known \textsc{Watchman Route} problem seeks a shortest route in a polygonal domain from which every point of the domain can be seen. In this paper, we study the cooperative variant of the problem, namely the \textsc{$k$-Watchmen…

This article considers the problem of conflict-free distribution of point-sized agents on a circular periphery encompassing all agents. The two key elements of the proposed policy include the construction of a set of convex layers (nested…

As machine learning agents act more autonomously in the world, they will increasingly interact with each other. Unfortunately, in many social dilemmas like the one-shot Prisoner's Dilemma, standard game theory predicts that ML agents will…

Given a simple polygon $P$ consisting of $n$ vertices, we study the problem of designing space-efficient algorithms for computing (i) the visibility polygon of a point inside $P$, (ii) the weak visibility polygon of a line segment inside…

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the…

This work addresses the challenge of patrolling regular grid graphs of any dimension using a single mobile agent with minimal memory and limited sensing range. We show that it is impossible to patrol some grid graphs with $0$ bits of…

We prove that every simply connected orthogonal polygon of $n$ vertices can be partitioned into $\left\lfloor\frac{3 n +4}{16}\right\rfloor$ (simply connected) orthogonal polygons of at most 8 vertices. It yields a new and shorter proof of…

We define and analyze a multi-agent multi-armed bandit problem in which decision-making agents can observe the choices and rewards of their neighbors. Neighbors are defined by a network graph with heterogeneous and stochastic…

Suppose an unpredictable evader is free to move around in a polygonal environment of arbitrary complexity that is under full camera surveillance. How many pursuers, each with the same maximum speed as the evader, are necessary and…

In this paper, we propose a new framework for multi-agent collaborative exploration of unknown environments. The proposed method combines state-of-the-art algorithms in mapping, safe corridor generation and multi-agent planning. It first…

We address the problem of distributed cooperative localization in wireless networks, i.e. nodes without prior position knowledge (agents) wish to determine their own positions. In non-cooperative approaches, positioning is only based on…

Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which…

Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms…