Related papers: Parallel Point-to-Point Shortest Paths and Batch Q…
A $(\beta,\epsilon)$-hopset for a weighted undirected $n$-vertex graph $G=(V,E)$ is a set of edges, whose addition to the graph guarantees that every pair of vertices has a path between them that contains at most $\beta$ edges, whose length…
In this paper, we study the MapReduce framework from an algorithmic standpoint and demonstrate the usefulness of our approach by designing and analyzing efficient MapReduce algorithms for fundamental sorting, searching, and simulation…
Long context training is crucial for LLM's context extension. Existing schemes, such as sequence parallelism, incur substantial communication overhead. Pipeline parallelism (PP) reduces this cost, but its effectiveness hinges on…
Given a directed, weighted graph $G=(V,E)$ undergoing edge insertions, the incremental single-source shortest paths (SSSP) problem asks for the maintenance of approximate distances from a dedicated source $s$ while optimizing the total time…
The All-Pairs Shortest Path problem (APSP) is one of the most central problems in distributed computation. In the CONGEST-CLIQUE model, in which $n$ nodes communicate with each other over a fully connected network by exchanging messages of…
The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…
Quality diversity (QD) algorithms have shown to provide sets of high quality solutions for challenging problems in robotics, games, and combinatorial optimisation. So far, theoretical foundational explaining their good behaviour in practice…
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental…
Although recent scientific output focuses on multiple shortest-path problem definitions for road networks, none of the existing solutions does efficiently answer all different types of SP queries. This work proposes SALT, a novel framework…
The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on $n$ vertices, no truly sub-cubic algorithms exist to compute APSP exactly even for undirected graphs. This is…
This paper introduces a novel algorithm combination designed for fast one-to-many multicriteria shortest path search. A preprocessing algorithm excludes irrelevant vertices by building a smaller cover graph. A modified version of…
Multi-Robot Path Planning (MRPP) on graphs, equivalently known as Multi-Agent Path Finding (MAPF), is a well-established NP-hard problem with critically important applications. As serial computation in (near)-optimally solving MRPP…
We study SINGLE-SOURCE SHORTEST PATH (SSSP) on unweighted intersection graphs whose node set corresponds to a set of $n$ constant-complexity objects in the plane. We prove SSSP can be solved in $O(U(n)\ \mathrm{polylog}\,n)$ expected time…
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…
Nearest neighbor search supports important applications in many domains, such as database, machine learning, computer vision. Since the computational cost for accurate search is too high, the community turned to the research of approximate…
Large-scale deep learning models contribute to significant performance improvements on varieties of downstream tasks. Current data and model parallelism approaches utilize model replication and partition techniques to support the…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set…
Graphs and their traversal is becoming significant as it is applicable to various areas of mathematics, science and technology. Various problems in fields as varied as biochemistry (genomics), electrical engineering (communication…
In this paper, we study the single-source shortest-path (SSSP) problem with positive edge weights, which is a notoriously hard problem in the parallel context. In practice, the $\Delta$-stepping algorithm proposed by Meyer and Sanders has…