Related papers: Sublinear-Time Maintenance of Breadth-First Spanni…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural…
Phylogenetic networks are a flexible model of evolution that can represent reticulate evolution and handle complex data. Tree-based networks, which are phylogenetic networks that have a spanning tree with the same root and leaf-set as the…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
Fischer has shown how to compute a minimum weight spanning tree of degree at most $b \Delta^* + \lceil \log\_b n\rceil$ in time $O(n^{4 + 1/\ln b})$ for any constant $b > 1$, where $\Delta^*$ is the value of an optimal solution and $n$ is…
We consider network design problems with deadline or delay. All previous results for these models are based on randomized embedding of the graph into a tree (HST) and then solving the problem on this tree. We show that this is not…
We prove that the local limit of the weighted spanning trees on any simple connected high degree almost regular sequence of electric networks is the Poisson(1) branching process conditioned to survive forever, by generalizing [NP22] and…
A maximal independent set (MIS) can be maintained in an evolving $m$-edge graph by simply recomputing it from scratch in $O(m)$ time after each update. But can it be maintained in time sublinear in $m$ in fully dynamic graphs? We answer…
Expander graphs are known to be robust to edge deletions in the following sense: for any online sequence of edge deletions $e_1, e_2, \ldots, e_k$ to an $m$-edge graph $G$ that is initially a $\phi$-expander, the algorithm can grow a set $P…
Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such…
We give an $m^{1+o(1)}\beta^{o(1)}$-time algorithm for generating a uniformly random spanning tree in an undirected, weighted graph with max-to-min weight ratio $\beta$. We also give an $m^{1+o(1)}\epsilon^{-o(1)}$-time algorithm for…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
We give the first almost-linear total time algorithm for deciding if a flow of cost at most $F$ still exists in a directed graph, with edge costs and capacities, undergoing decremental updates, i.e., edge deletions, capacity decreases, and…
Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on…
We present a work-efficient parallel level-synchronous Breadth First Search (BFS) algorithm for shared-memory architectures which achieves the theoretical lower bound on parallel running time. The optimality holds regardless of the shape of…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
In the decremental single-source shortest paths (SSSP) problem, the input is an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges undergoing edge deletions, together with a fixed source vertex $s\in V$. The goal is to maintain a…
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and…
We present an implementation and an experimental evaluation of an algorithm that, given a connected graph G (represented by adjacency lists), estimates in sublinear time, with a relative error, the Minimum Spanning Tree Weight of G; the…