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We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…

Data Structures and Algorithms · Computer Science 2018-03-02 Monika Henzinger , Sebastian Krinninger , Danupon Nanongkai

The \emph{Steiner tree} problem is one of the fundamental and classical problems in combinatorial optimization. In this paper, we study this problem in the $\mathcal{CONGESTED}$ $\mathcal{CLIQUE}$ model of distributed computing and present…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-31 Parikshit Saikia , Sushanta Karmakar

There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so…

Computational Complexity · Computer Science 2019-05-21 Michael Dinitz , Yasamin Nazari , Zeyu Zhang

Given a compact $E \subset \mathbb{R}^n$ and $s > 0$, the maximum distance problem seeks a compact and connected subset of $\mathbb{R}^n$ of smallest one dimensional Hausdorff measure whose $s$-neighborhood covers $E$. For $E\subset…

Classical Analysis and ODEs · Mathematics 2021-03-12 Enrique G. Alvarado , Bala Krishnamoorthy , Kevin R. Vixie

Given a point set $P$ in the Euclidean space, a geometric $t$-spanner $G$ is a graph on $P$ such that for every pair of points, the shortest path in $G$ between those points is at most a factor $t$ longer than the Euclidean distance between…

Computational Geometry · Computer Science 2024-12-10 Kevin Buchin , Carolin Rehs , Torben Scheele

We settle the pseudo-polynomial complexity of the Demand Strip Packing (DSP) problem: Given a strip of fixed width and a set of items with widths and heights, the items must be placed inside the strip with the objective of minimizing the…

Data Structures and Algorithms · Computer Science 2025-07-02 Klaus Jansen , Malin Rau , Malte Tutas

We introduce the $st$-cut version the Sparsest-Cut problem, where the goal is to find a cut of minimum sparsity among those separating two distinguished vertices $s,t\in V$. Clearly, this problem is at least as hard as the usual (non-$st$)…

Data Structures and Algorithms · Computer Science 2016-09-26 Robert Krauthgamer , Tal Wagner

In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…

Data Structures and Algorithms · Computer Science 2024-06-21 Yu Cheng , Max Li , Honghao Lin , Zi-Yi Tai , David P. Woodruff , Jason Zhang

We study the problem of releasing the weights of all-pair shortest paths in a weighted undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed and two graphs are neighbors if their edge weights differ…

Data Structures and Algorithms · Computer Science 2022-03-31 Badih Ghazi , Ravi Kumar , Pasin Manurangsi , Jelani Nelson

For a positive integer $t$ and a graph $G$, an additive $t$-spanner of $G$ is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus $t$. Minimum Additive $t$-Spanner Problem is to…

Data Structures and Algorithms · Computer Science 2019-03-05 Yusuke Kobayashi

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…

Data Structures and Algorithms · Computer Science 2018-08-08 Takuro Fukunaga , Takanori Maehara

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

Data Structures and Algorithms · Computer Science 2025-09-10 Shangqi Lu , Yufei Tao

Emerging optical and virtualization technologies enable the design of more flexible and demand-aware networked systems, in which resources can be optimized toward the actual workload they serve. For example, in a demand-aware datacenter…

Networking and Internet Architecture · Computer Science 2023-08-22 Aleksander Figiel , Janne H. Korhonen , Neil Olver , Stefan Schmid

The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph $G$. Our goal is to find a spanning subgraph $S$ of $G$ with the…

Data Structures and Algorithms · Computer Science 2025-07-02 Miguel Bosch-Calvo , Fabrizio Grandoni , Afrouz Jabal Ameli

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…

Data Structures and Algorithms · Computer Science 2015-07-03 MohammadTaghi Hajiaghayi , Guy Kortsarz , Robert MacDavid , Manish Purohit , Kanthi Sarpatwar

We consider the problem of constructing a single spanning tree for the single-source buy-at-bulk network design problem for doubling-dimension graphs. We compute a spanning tree to route a set of demands (or data) along a graph to or from a…

Data Structures and Algorithms · Computer Science 2010-04-05 Srivathsan Srinivasagopalan , Costas Busch , S. S. Iyengar

Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which…

Data Structures and Algorithms · Computer Science 2021-06-07 Michael Kapralov , Robert Krauthgamer , Jakab Tardos , Yuichi Yoshida

Finding the maximum number of disjoint spanning trees in a given graph is a well-studied problem with several applications and connections. The Tutte-Nash-Williams theorem provides a min-max relation for this problem which also extends to…

Data Structures and Algorithms · Computer Science 2025-03-27 Karthekeyan Chandrasekaran , Chandra Chekuri , Weihao Zhu

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…

Data Structures and Algorithms · Computer Science 2007-07-10 Noga Alon , Fedor V. Fomin , Gregory Gutin , Michael Krivelevich , Saket Saurabh

We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…

Computational Geometry · Computer Science 2016-03-22 Glencora Borradaile , David Eppstein