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Approximation algorithms for solving the line-capacitated minimum Steiner tree problem
In this paper, we address the line-capacitated minimum Steiner tree problem (the Lc-MStT problem, for short), which is a variant of the (Euclidean)...
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Correction to: Stronger MIP formulations for the Steiner forest problem
A correction to this paper has been published: https://doi.org/10.1007/s10107-021-01648-9
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Structural Properties of Minimum Multi-source Multi-Sink Steiner Networks in the Euclidean Plane
Given two finite sets A and B of points in the Euclidean plane, a minimum multi-source multi-sink Steiner network in the plane, or a minimum ( A , B )-ne...
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Implications, conflicts, and reductions for Steiner trees
The Steiner tree problem in graphs (SPG) is one of the most studied problems in combinatorial optimization. In the past 10 years, there have been...
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Stronger MIP formulations for the Steiner forest problem
The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. We propose new cut- and flow-based integer...
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The m-Steiner Traveling Salesman Problem with online edge blockages
We consider the online multiple Steiner Traveling Salesman Problem based on the background of the delivery of packages in an urban traffic network....
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Approximation of Steiner forest via the bidirected cut relaxation
The classical algorithm of Agrawal et al. (SIAM J Comput 24(3):440–456,
1995 ), stated in the setting of the primal-dual schema by Goemans and...
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Node connectivity augmentation via iterative randomized rounding
Many network design problems deal with the design of low-cost networks that are resilient to the failure of their elements (such as nodes or links)....
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Cost Sharing, Capacity Investment and Pricing in Networks
Anja Schedel analyzes two models in the field of algorithmic game theory which both constitute bilevel problems in networks. The first model is a...
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Oriented Cycles in Digraphs of Large Outdegree
In 1985, Mader conjectured that for every acyclic digraph F there exists K = K ( F ) such that every digraph D with minimum out-degree at least K ...
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A unified approach to approximate partial, prize-collecting, and budgeted sweep cover problems
In a sweep cover problem, mobile sensors move around to collect information from positions of interest (PoIs) periodically and timely. A PoI is sweep-covered...
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Locating Service and Charging Stations
In this paper, we consider the problem of locating service and charging stations to serve commuters. In the service station location problem we are...
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A fast \((2 + \frac{2}{7})\)-approximation algorithm for capacitated cycle covering
We consider the capacitated cycle covering problem : given an undirected, complete graph G with metric edge lengths and demands on the vertices, we...
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Tight Algorithms for Connectivity Problems Parameterized by Modular-Treewidth
We study connectivity problems from a fine-grained parameterized perspective. Cygan et al. (TALG 2022) first obtained algorithms with...
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Lasserre Integrality Gaps for Graph Spanners and Related Problems
There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a...
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Placing Green Bridges Optimally, with a Multivariate Analysis
We study the problem of placing wildlife crossings, such as green bridges, over human-made obstacles to challenge habitat fragmentation. The main...
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The GeoSteiner software package for computing Steiner trees in the plane: an updated computational study
The GeoSteiner software package has for about 20 years been the fastest (publicly available) program for computing exact solutions to Steiner tree...
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Stable volumes for persistent homology
This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent...
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Introduction
In this chapter, we introduce and motivate the topics of this thesis, and describe the obtained results.