Related papers: Dynamic Low-Stretch Trees via Dynamic Low-Diameter…
With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…
Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\"ive solution is to iteratively find the densest subgraph and remove it in…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
Loop nesting forests (LNFs) are a fundamental abstraction for reasoning about control-flow structure, enabling applications such as compiler optimizations, program analysis, and dominator computation. While efficient static algorithms for…
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…
Low Diameter Decompositions (LDDs) are invaluable tools in the design of combinatorial graph algorithms. While historically they have been applied mainly to undirected graphs, in the recent breakthrough for the negative-length Single Source…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches…
We study spanners in planar domains, including polygonal domains, polyhedral terrain, and planar metrics. Previous work showed that for any constant $\epsilon\in (0,1)$, one could construct a $(2+\epsilon)$-spanner with $O(n\log(n))$ edges…
Connectivity queries, which check whether vertices belong to the same connected component, are fundamental in graph computations. Sliding window connectivity processes these queries over sliding windows, facilitating real-time streaming…
Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…
The $k$d-tree is one of the most widely used data structures to manage multi-dimensional data. Due to the ever-growing data volume, it is imperative to consider parallelism in $k$d-trees. However, we observed challenges in existing parallel…
We study smoothed analysis of distributed graph algorithms, focusing on the fundamental minimum spanning tree (MST) problem. With the goal of studying the time complexity of distributed MST as a function of the "perturbation" of the input…
The dynamic set cover problem has been subject to growing research attention in recent years. In this problem, we are given as input a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element appears…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…