Related papers: Customizable Contraction Hierarchies
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
The restoration lemma by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [Dist. Comp. '02] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two…
The Dijkstra algorithm is a classical method for solving the shortest path problem on weighted graphs. There are several variations of the Dijkstra algorithm, including algorithms for the widest path problem and for two-player games. In…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
For minimally rigid graphs, the same edge-length data can admit multiple realizations (up to translations and rotations). Finding graphs with exceptionally many realizations is an extremal problem in rigidity theory, but exhaustive search…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…
This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…
We study a class of nested path problems, in which every path-based variable can be decomposed into a sequence of subpaths. Subpaths must satisfy local resources, while paths must satisfy additional global resources. This paper develops a…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
The classic problem of constrained pathfinding is a well-studied, yet challenging, topic in AI with a broad range of applications in various areas such as communication and transportation. The Weight Constrained Shortest Path Problem…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…