Related papers: Robust Shortest Path Planning and Semicontractive …
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
A common technique to speed up shortest path queries in graphs is to use a bidirectional search, i.e., performing a forward search from the start and a backward search from the destination until a common vertex on a shortest path is found.…
In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival,…
The Minimum Path Cover (MPC) problem consists of finding a minimum-cardinality set of node-disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on acyclic digraphs (DAGs) where, given a subset of…
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset…
The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…
The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
Spurred by the growth of transportation network companies and increasing data capabilities, vehicle routing and ride-matching algorithms can improve the efficiency of private transportation services. However, existing routing solutions do…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded…
We present the Goal Uncertain Stochastic Shortest Path (GUSSP) problem -- a general framework to model path planning and decision making in stochastic environments with goal uncertainty. The framework extends the stochastic shortest path…
In this paper, we give a new framework for the stochastic shortest path problem in finite state and action spaces. Our framework generalizes both the frameworks proposed by Bertsekas and Tsitsikli and by Bertsekas and Yu. We prove that the…