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We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…

Data Structures and Algorithms · Computer Science 2021-07-19 Julián Mestre , Sergey Pupyrev , Seeun William Umboh

We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM,…

Optimization and Control · Mathematics 2007-05-23 Yichuan Ding , Nathan Krislock , Jiawei Qian , Henry Wolkowicz

In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-13 Lélia Blin , Maria Gradinariu Potop-Butucaru , Stephane Rovedakis

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We…

Neural and Evolutionary Computing · Computer Science 2014-01-10 Dogan Corus , Per Kristian Lehre , Frank Neumann , Mojgan Pourhassan

We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…

Computational Complexity · Computer Science 2019-10-02 Jan Dreier , Janosch Fuchs , Tim A. Hartmann , Philipp Kuinke , Peter Rossmanith , Bjoern Tauer , Hung-Lung Wang

A rectilinear Steiner tree for a set $P$ of points in $\mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree…

Computational Geometry · Computer Science 2021-03-16 Henk Alkema , Mark de Berg

We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph $G=(V,E,w)$, where $V=\{r\}\cup S \cup T$, and an integer $k$, the goal is to find a minimum cost subgraph of $G$ in which there are…

Data Structures and Algorithms · Computer Science 2024-07-11 Sarel Cohen , Lior Kamma , Aikaterini Niklanovits

The hop-constrained Steiner tree problem (HSTP) is a generalization of the classical Steiner tree problem. It asks for a minimum cost subtree that spans some specified nodes of a given graph, such that the number of edges between each node…

Data Structures and Algorithms · Computer Science 2021-11-16 Adalat Jabrayilov

We consider an important generalization of the Steiner tree problem, the \emph{Steiner forest problem}, in the Euclidean plane: the input is a multiset $X \subseteq \mathbb{R}^2$, partitioned into $k$ color classes $C_1, C_2, \ldots, C_k…

Data Structures and Algorithms · Computer Science 2024-05-14 Artur Czumaj , Shaofeng H. -C. Jiang , Robert Krauthgamer , Pavel Veselý

A Euclidean noncrossing Steiner $(1+\epsilon)$-spanner for a point set $P\subset\mathbb{R}^2$ is a planar straight-line graph that, for any two points $a, b \in P$, contains a path whose length is at most $1+\epsilon$ times the Euclidean…

Computational Geometry · Computer Science 2026-02-23 Sujoy Bhore , Sándor Kisfaludi-Bak , Lazar Milenković , Csaba D. Tóth , Karol Węgrzycki , Sampson Wong

We study the parameterized complexity of the directed variant of the classical {\sc Steiner Tree} problem on various classes of directed sparse graphs. While the parameterized complexity of {\sc Steiner Tree} parameterized by the number of…

Data Structures and Algorithms · Computer Science 2012-10-02 Mark Jones , Daniel Lokshtanov , M. S. Ramanujan , Saket Saurabh , Ondřej Suchý

The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…

Optimization and Control · Mathematics 2020-05-26 Alexandre Salles da Cunha

The Weighted Tree Augmentation Problem (WTAP) is a fundamental well-studied problem in the field of network design. Given an undirected tree $G=(V,E)$, an additional set of edges $L \subseteq V\times V$ disjoint from $E$ called…

Data Structures and Algorithms · Computer Science 2016-09-16 David Adjiashvili

We propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted graph…

Data Structures and Algorithms · Computer Science 2017-07-12 Marcin Pilipczuk , Michał Pilipczuk , Piotr Sankowski , Erik Jan van Leeuwen

We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…

Computational Geometry · Computer Science 2019-03-12 Irina Kostitsyna , Maarten Löffler , Valentin Polishchuk , Frank Staals

We consider the following geometric optimization problem: Given $ n $ axis-aligned rectangles in the plane, the goal is to find a set of horizontal segments of minimum total length such that each rectangle is stabbed. A segment stabs a…

Computational Geometry · Computer Science 2021-07-15 Friedrich Eisenbrand , Martina Gallato , Ola Svensson , Moritz Venzin

A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. In this paper we study Minimum Stable Cut, the problem of finding a stable cut of minimum weight. Since this…

Computational Complexity · Computer Science 2026-04-08 Michael Lampis

Although Software-Defined Networking (SDN) enables flexible network resource allocations for traffic engineering, current literature mostly focuses on unicast communications. Compared to traffic engineering for multiple unicast flows,…

Networking and Internet Architecture · Computer Science 2016-01-27 Liang-Hao Huang , Hsiang-Chun Hsu , Shan-Hsiang Shen , De-Nian Yang , Wen-Tsuen Chen

In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…

Computational Geometry · Computer Science 2020-05-13 Tanaeem M. Moosa , M. Sohel Rahman

We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…

Data Structures and Algorithms · Computer Science 2026-05-05 Narek Bojikian , Alexander Firbas , Robert Ganian , Hung P. Hoang , Krisztina Szilágyi