相关论文: Near-Optimal Decremental Hopsets with Applications

We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…

For any constants $d\ge 1$, $\epsilon >0$, $t>1$, and any $n$-point set $P\subset\mathbb{R}^d$, we show that there is a geometric graph $G=(P,E)$ having $O(n\log^2 n\log\log n)$ edges with the following property: For any $F\subseteq P$,…

We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…

We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…

Given parameters $\alpha\geq 1,\beta\geq 0$, a subgraph $G'=(V,H)$ of an $n$-vertex unweighted undirected graph $G=(V,E)$ is called an $(\alpha,\beta)$-spanner if for every pair $u,v\in V$ of vertices, $d_{G'}(u,v)\leq \alpha…

Genome assembly is a fundamental problem in Bioinformatics, where for a given set of overlapping substrings of a genome, the aim is to reconstruct the source genome. The classical approaches to solving this problem use assembly graphs, such…

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…

In the Single Source Replacement Paths (SSRP) problem we are given a graph $G = (V, E)$, and a shortest paths tree $\widehat{K}$ rooted at a node $s$, and the goal is to output for every node $t \in V$ and for every edge $e$ in…

In this paper, we present a new randomized $O(1)$-approximation algorithm for the All-Pairs Shortest Paths (APSP) problem in weighted undirected graphs that runs in just $O(\log \log \log n)$ rounds in the Congested-Clique model. Before our…

The fundamental sparsest cut problem takes as input a graph $G$ together with the edge costs and demands, and seeks a cut that minimizes the ratio between the costs and demands across the cuts. For $n$-node graphs~$G$ of treewidth~$k$,…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

The Discrepancy of a hypergraph is the minimum attainable value, over two-colorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a…

For a hereditary graph class $\mathcal{H}$, the $\mathcal{H}$-elimination distance of a graph $G$ is the minimum number of rounds needed to reduce $G$ to a member of $\mathcal{H}$ by removing one vertex from each connected component in each…

We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…

We describe a simple deterministic $O( \varepsilon^{-1} \log \Delta)$ round distributed algorithm for $(2\alpha+1)(1 + \varepsilon)$ approximation of minimum weighted dominating set on graphs with arboricity at most $\alpha$. Here $\Delta$…

The Planar Graph Metric Compression Problem is to compactly encode the distances among $k$ nodes in a planar graph of size $n$. Two na\"ive solutions are to store the graph using $O(n)$ bits, or to explicitly store the distance matrix with…

In a recent breakthrough work, Gartland and Lokshtanov [FOCS 2020] showed a quasi-polynomial-time algorithm for Maximum Weight Independent Set in $P_t$-free graphs, that is, graphs excluding a fixed path as an induced subgraph. Their…

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in…

In the Edge-Disjoint Paths with Congestion problem (EDPwC), we are given an undirected n-vertex graph G, a collection M={(s_1,t_1),...,(s_k,t_k)} of demand pairs and an integer c. The goal is to connect the maximum possible number of the…

We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3}…