Related papers: Parallel Algorithms for Geometric Graph Problems
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
For two multisets $S$ and $T$ of points in $[\Delta]^2$, such that $|S| = |T|= n$, the earth-mover distance (EMD) between $S$ and $T$ is the minimum cost of a perfect bipartite matching with edges between points in $S$ and $T$, i.e.,…
The Traveling Salesman Problem (TSP) is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on…
In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…
We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take $poly(\log{\log{n}})$ rounds in the near-linear memory MPC model. Our results are for…
In the minimum spanning tree (MST) interdiction problem, we are given a graph $G=(V,E)$ with edge weights, and want to find some $X\subseteq E$ satisfying a knapsack constraint such that the MST weight in $(V,E\setminus X)$ is maximized.…
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…
We consider two natural variants of the problem of minimum spanning tree (MST) of a graph in the parallel setting: MST verification (verifying if a given tree is an MST) and the sensitivity analysis of an MST (finding the lowest cost…
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…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Existing approaches for graph neural networks commonly suffer from the oversmoothing issue, regardless of how neighborhoods are aggregated. Most methods also focus on transductive scenarios for fixed graphs, leading to poor generalization…
We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition.…
Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
This paper presents a novel extended dynamic programming approach for energy minimization (EDP) to solve the correspondence problem for stereo and motion. A significant speedup is achieved using a recursive minimum search strategy (RMS).…
Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.…
Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…