Related papers: Improved Worst-Case Deterministic Parallel Dynamic…
In this paper we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in several graph classes of bounded width. The problem takes an edge-weighted graph and pairs of vertices as input, and…
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…
We study the parallel complexity of finding a basis of a graphic matroid under independence-oracle access. Karp, Upfal, and Wigderson (FOCS 1985, JCSS 1988) initiated the study of this problem and established two algorithms for finding a…
We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose…
We present new deterministic algorithms for computing distributed weighted minimum weight cycle (MWC) in undirected and directed graphs and distributed weighted all nodes shortest cycle (ANSC) in directed graphs. Our algorithms for these…
We present a deterministic near-linear time algorithm that computes the edge-connectivity and finds a minimum cut for a simple undirected unweighted graph G with n vertices and m edges. This is the first o(mn) time deterministic algorithm…
Real-world networks are prone to breakdowns. Typically in the underlying graph $G$, besides the insertion or deletion of edges, the set of active vertices changes overtime. A vertex might work actively, or it might fail, and gets isolated…
We propose a simple and natural approximation algorithm for the problem of finding a 2-edge-connected spanning subgraph of minimum total edge cost in a graph. The algorithm maintains a spanning forest starting with an empty edge set. In…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
Dynamically maintaining the minimum cut in a graph $G$ under edge insertions and deletions is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an $n$-node graph the…
The shortest path problem is a typical problem in graph theory with wide potential applications. The state-of-the-art single-source shortest paths algorithm on the weight graph is the $\Delta$-stepping algorithm, which can efficiently…
Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we…
Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…
We provide an algorithm that maintains, against an adaptive adversary, a $(1-\varepsilon)$-approximate maximum matching in $n$-node $m$-edge general (not necessarily bipartite) undirected graph undergoing edge deletions with high…
We present the first near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in a graph, while previous parallel algorithms with poly-logarithmic depth required at least quadratic work in the number of vertices. In…
We consider the ``minimum degree spanning tree'' problem. As input, we receive an undirected, connected graph $G=(V, E)$ with $n$ nodes and $m$ edges, and our task is to find a spanning tree $T$ of $G$ that minimizes $\max_{u \in V}…
We present a new algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of any (non-negatively) real-weighted graph $G = (V,E,\omega)$. As an intermediate step, we use a new, fast, linear-time…
We present a deterministic incremental algorithm for \textit{exactly} maintaining the size of a minimum cut with $\widetilde{O}(1)$ amortized time per edge insertion and $O(1)$ query time. This result partially answers an open question…
Computing \emph{all best swap edges} (ABSE) of a spanning tree $T$ of a given $n$-vertex and $m$-edge undirected and weighted graph $G$ means to select, for each edge $e$ of $T$, a corresponding non-tree edge $f$, in such a way that the…
The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and…