Related papers: A Deterministic Almost-Linear Time Algorithm for M…
In recent years, there has been a growing interest in solving various graph coloring problems in the streaming model. The initial algorithms in this line of work are all crucially randomized, raising natural questions about how important a…
We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds. This answers one of the…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
We present deterministic algorithms for maintaining a $(3/2 + \epsilon)$ and $(2 + \epsilon)$-approximate maximum matching in a fully dynamic graph with worst-case update times $\hat{O}(\sqrt{n})$ and $\tilde{O}(1)$ respectively. The…
We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with $\tilde{O}(mn^{4/5})$ worst-case update time processing arbitrary $s,t$-distance queries…
In this paper, we consider algorithms for edge-coloring multigraphs $G$ of bounded maximum degree, i.e., $\Delta(G) = O(1)$. Shannon's theorem states that any multigraph of maximum degree $\Delta$ can be properly edge-colored with…
In this paper, we present an improved algorithm for the maximum flow problem on general networks with $n$ vertices and $m$ arcs. We show how to solve the problem in $O(mn)$ time, when $m = O(n^{2-\epsilon})$, for some $0 <\epsilon \leq 1$.…
We present a simple and faster algorithm for computing fair cuts on undirected graphs, a concept introduced in recent work of Li et al. (SODA 2023). Informally, for any parameter $\epsilon>0$, a $(1+\epsilon)$-fair $(s,t)$-cut is an…
It is known that a better than $2$-approximation algorithm for the girth in dense directed unweighted graphs needs $n^{3-o(1)}$ time unless one uses fast matrix multiplication. Meanwhile, the best known approximation factor for a…
We present deterministic constant-round protocols for the graph connectivity problem in the model where each of the $n$ nodes of a graph receives a row of the adjacency matrix, and broadcasts a single sublinear size message to all other…
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first…
We present a deterministic fully-dynamic data structure for maintaining information about the bridges in a graph. We support updates in $\tilde{O}((\log n)^2)$ amortized time, and can find a bridge in the component of any given vertex, or a…
Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…
In the last few years the so--called "linear deterministic" model of relay channels has gained popularity as a means of studying the flow of information over wireless communication networks, and this approach generalizes the model of…
The minimum cost flow problem is one of the most studied network optimization problems and appears in numerous applications. Some efficient algorithms exist for this problem, which are freely available in the form of libraries or software…
We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily…
We design an $n^{2+o(1)}$-time algorithm that constructs a cut-equivalent (Gomory-Hu) tree of a simple graph on $n$ nodes. This bound is almost-optimal in terms of $n$, and it improves on the recent $\tilde{O}(n^{2.5})$ bound by the authors…
In an undirected graph, a $k$-cut is a set of edges whose removal breaks the graph into at least $k$ connected components. The minimum weight $k$-cut can be computed in $O(n^{O(k)})$ time, but when $k$ is treated as part of the input,…
We give an $O(k^3 n \log n \min(k,\log^2 n) \log^2(nC))$-time algorithm for computing maximum integer flows in planar graphs with integer arc {\em and vertex} capacities bounded by $C$, and $k$ sources and sinks. This improves by a factor…
In this paper we study flow problems on temporal networks, where edge capacities and travel times change over time. We consider a network with $n$ nodes and $m$ edges where the capacity and length of each edge is a piecewise constant…