Related papers: Distributed Approximation Algorithms for the Combi…
We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian…
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on $n$ vertices whose edge weights are chosen independently and uniformly at random from $[0,1]$ is $O(n^2)$, in expectation and with high…
We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
We study the broadcast version of the CONGEST CLIQUE model of distributed computing. In this model, in each round, any node in a network of size $n$ can send the same message (i.e. broadcast a message) of limited size to every other node in…
The fundamental sparsest cut problem takes as input a graph $G$ together with the edge costs and demands, and seeks a cut that minimizes the ratio between the costs and demands across the cuts. For $n$-node graphs~$G$ of treewidth~$k$,…
Solving a collision-aware multi-agent mission planning (task allocation and path finding) problem is challenging due to the requirement of real-time computational performance, scalability, and capability of handling static/dynamic obstacles…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
The Split algorithm is an essential building block of route-first cluster-second heuristics and modern genetic algorithms for vehicle routing problems. The algorithm is used to partition a solution, represented as a giant tour without…
We analyze two communication-efficient algorithms for distributed statistical optimization on large-scale data sets. The first algorithm is a standard averaging method that distributes the $N$ data samples evenly to $\nummac$ machines,…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by…
In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…
The classical multi-agent rendezvous problem asks for a deterministic algorithm by which $n$ points scattered in a plane can move about at constant speed and merge at a single point, assuming each point can use only the locations of the…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed…
Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm…
The path version of the Traveling Salesman Problem is one of the most well-studied variants of the ubiquitous TSP. Its generalization, the Multi-Path TSP, has recently been used in the best known algorithm for path TSP by Traub and Vygen…