Related papers: Shortest-Path FFT: Optimal SIMD Instruction Schedu…
This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…
We consider the problem of computing shortest paths in weighted unit-disk graphs in constant dimension $d$. Although the single-source and all-pairs variants of this problem are well-studied in the plane case, no non-trivial exact distance…
Learning latent costs of transitions on graphs from trajectories demonstrations under various contextual features is challenging but useful for path planning. Yet, existing methods either oversimplify cost assumptions or scale poorly with…
We consider the bi-criteria shortest-path problem where we want to compute shortest paths on a graph that simultaneously balance two cost functions. While this problem has numerous applications, there is usually no path minimizing both cost…
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…
Graphs have become a key tool when modeling and solving problems in different areas. The Floyd-Warshall (FW) algorithm computes the shortest path between all pairs of vertices in a graph and is employed in areas like communication…
We present a work-efficient parallel level-synchronous Breadth First Search (BFS) algorithm for shared-memory architectures which achieves the theoretical lower bound on parallel running time. The optimality holds regardless of the shape of…
Graph data models are widely used in many areas, for example, bioinformatics, graph databases. In these areas, it is often required to process queries for large graphs. Some of the most common graph queries are navigational queries. The…
Contraction Hierarchies is a successful speedup-technique to Dijkstra's seminal shortest path algorithm that has a convenient trade-off between preprocessing and query times. We investigate a shared-memory parallel implementation that uses…
We consider the problem of designing succinct data structures for interval graphs with $n$ vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time in the $\Theta(\log n)$-bit word RAM model. The…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
This paper addresses distributed stochastic optimization problems under non-i.i.d. data, focusing on the inherent trade-offs between communication and computational efficiency. To this end, we propose FlexGT, a flexible snapshot gradient…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
To find a shortest path between two nodes $s_0$ and $s_1$ in a given graph, a classical approach is to start a Breadth-First Search (BFS) from $s_0$ and run it until the search discovers $s_1$. Alternatively, one can start two Breadth-First…
We design a space-efficient algorithm for performing depth-first search traversal(DFS) of a graph in $O(m+n\log^* n)$ time using $O(n)$ bits of space. While a normal DFS algorithm results in a DFS-tree (in case the graph is connected), our…
We present an algorithm for a fault tolerant Depth First Search (DFS) Tree in an undirected graph. This algorithm is drastically simpler than the current state-of-the-art algorithms for this problem, uses optimal space and optimal…
Learning graphical conditional independence structures is an important machine learning problem and a cornerstone of causal discovery. However, the accuracy and execution time of learning algorithms generally struggle to scale to problems…
In recent years, deep neural networks (DNNs) have gained widespread adoption for continuous mobile object detection (OD) tasks, particularly in autonomous systems. However, a prevalent issue in their deployment is the one-size-fits-all…
We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph $G$ on $n$ vertices can be partitioned into a set of $O(n/r)$ edge-disjoint regions (called an $r$-division) with $O(r)$ vertices each,…