相关论文: Hunter, Cauchy Rabbit, and Optimal Kakeya Sets
The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…
This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest…
First-order adaptive optimization methods like Adam are the default choices for training modern deep neural networks. Despite their empirical success, the theoretical understanding of these methods in non-smooth settings, particularly in…
Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the tracking paths problem is that of finding the smallest subset of vertices in $G$ whose intersection with any $s$-$t$ path results in a unique sequence. This problem is…
We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed…
We present a simple model to study L\'{e}vy-flight foraging in a finite landscape with countable targets. In our approach, foraging is a step-based exploratory random search process with a power-law step-size distribution $P(l) \propto…
We consider a swarm of $n$ robots in \mathbb{R}^d. The robots are oblivious, disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering…
We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. In our stochastic simulations, individuals may move strategically towards the direction with more…
This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission…
The higher-order orthogonality iteration (HOOI) has been popularly used for finding a best low-multilinear-rank approximation of a tensor. However, its iterate sequence convergence is still an open question. In this paper, we first analyze…
A sorting network is a shortest path from 12..n to n..21 in the Cayley graph of the symmetric group S(n) generated by nearest-neighbor swaps. A pattern is a sequence of swaps that forms an initial segment of some sorting network. We prove…
We introduce a model of a controlled random graph process. In this model, the edges of the complete graph $K_n$ are ordered randomly and then revealed, one by one, to a player called Builder. He must decide, immediately and irrevocably,…
This paper presents a search-based partial motion planner to generate dynamically feasible trajectories for car-like robots in highly dynamic environments. The planner searches for smooth, safe, and near-time-optimal trajectories by…
The Kakeya conjecture is generally formulated as one the following statements: every compact/Borel/arbitrary subset of ${\mathbb R}^n$ that contains a (unit) line segment in every direction has Hausdorff dimension $n$; or, sometimes, that…
This paper develops a planner to find an optimal assembly sequence to assemble several objects. The input to the planner is the mesh models of the objects, the relative poses between the objects in the assembly, and the final pose of the…
The Competing Bandits framework is a recently emerging area that integrates multi-armed bandits in online learning with stable matching in game theory. While conventional models assume that all players and arms are constantly available, in…
In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of…
We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…
In collective tree exploration, a team of $k$ mobile agents is tasked to go through all edges of an unknown tree as fast as possible. An edge of the tree is revealed to the team when one agent becomes adjacent to that edge. The agents start…
We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…