Related papers: $A^*$ for Graphs of Convex Sets
We present the `Basic S*' algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, $G$, which is constructed as a discrete representation of an underlying configuration space (a larger…
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes…
Constrained pathfinding is a well-studied, yet challenging network optimisation problem that can be seen in a broad range of real-world applications. Pathfinding with multiple resource limits, which is known as the Resource Constrained…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
We present successive convexification, a real-time-capable solution method for nonconvex trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence, that only requires first-order information. The…
This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on…
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper,…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
We study the decremental All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. The input to the problem is an $n$-vertex $m$-edge graph $G$ with non-negative edge lengths, that undergoes a sequence of edge deletions.…
Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning…
Given a directed graph $G$ with arbitrary real-valued weights, the single source shortest-path problem (SSSP) asks for, given a source $s$ in $G$, finding a shortest path from $s$ to each vertex $v$ in $G$. A classical SSSP algorithm…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Path planning for wheeled mobile robots is a critical component in the field of automation and intelligent transportation systems. Car-like vehicles, which have non-holonomic constraints on their movement capability impose additional…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…