Related papers: Optimal algebraic Breadth-First Search for sparse …
Graph-searching algorithms play a crucial role in various computational domains, enabling efficient exploration and pathfinding in structured data. Traditional approaches, such as Depth-First Search (DFS) and Breadth-First Search (BFS),…
ANNS for embedded vector representations of texts is commonly used in information retrieval, with two important information representations being sparse and dense vectors. While it has been shown that combining these representations…
The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of…
Mining maximal subgraphs with cohesive structures from a bipartite graph has been widely studied. One important cohesive structure on bipartite graphs is k-biplex, where each vertex on one side disconnects at most k vertices on the other…
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering…
In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB)…
We initiate the study of approximation algorithms and computational barriers for constructing sparse $\alpha$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an…
For parallel breadth first search (BFS) algorithm on large-scale distributed memory systems, communication often costs significantly more than arithmetic and limits the scalability of the algorithm. In this paper we sufficiently reduce the…
In graph sparsification, the goal has almost always been of {global} nature: compress a graph into a smaller subgraph ({sparsifier}) that maintains certain features of the original graph. Algorithms can then run on the sparsifier, which in…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
Breadth First Search (BFS) and other graph traversal techniques are widely used for measuring large unknown graphs, such as online social networks. It has been empirically observed that an incomplete BFS is biased toward high degree nodes.…
Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…
Enumerating consistent global states of a computation is a fundamental problem in parallel computing with applications to debug- ging, testing and runtime verification of parallel programs. Breadth-first search (BFS) enumeration is…
We propose a novel algorithm for enumerating and listing all minimal cutsets of a given graph. It is known that this problem is NP-hard. We use connectivity properties of a given graph to develop an algorithm with reduced complexity for…
For any undirected graph $G=(V,E)$ and a set $E_W$ of candidate edges with $E\cap E_W=\emptyset$, the $(k,\gamma)$-spectral augmentability problem is to find a set $F$ of $k$ edges from $E_W$ with appropriate weighting, such that the…
We provide the first approximation quality guarantees for the Cuthull-McKee heuristic for reordering symmetric matrices to have low bandwidth, and we provide an algorithm for reconstructing bounded-bandwidth graphs from distance oracles…
Preference restrictions have played a significant role in computational social choice. This paper studies a framework that connects preference restrictions with classical graph search paradigms. We model candidates as vertices of a graph…
Graphs are central to modeling relationships in scientific computing, data analysis, and AI/ML, but their growing scale can exceed the memory and compute capacity of single nodes, requiring distributed solutions. Existing distributed graph…
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…