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We revisit the a priori TSP (with independent activation) and prove stronger approximation guarantees than were previously known. In the a priori TSP, we are given a metric space $(V,c)$ and an activation probability $p(v)$ for each…

Data Structures and Algorithms · Computer Science 2023-09-20 Jannis Blauth , Meike Neuwohner , Luise Puhlmann , Jens Vygen

In a Subgraph Problem we are given some graph and want to find a feasible subgraph that optimizes some measure. We consider Multistage Subgraph Problems (MSPs), where we are given a sequence of graph instances (stages) and are asked to find…

Data Structures and Algorithms · Computer Science 2023-06-16 Markus Chimani , Niklas Troost , Tilo Wiedera

The (1,2)-TSP is a special case of the TSP where each edge has cost either 1 or 2. In this paper we give a lower bound of $\frac{3}{2}$ for the approximation ratio of the 2-Opt algorithm for the (1,2)-TSP. Moreover, we show that the 3-Opt…

Discrete Mathematics · Computer Science 2021-05-24 Xianghui Zhong

A well-studied continuous model of graphs considers each edge as a continuous unit-length interval of points. In the problem $\delta$-Tour defined within this model, the objective to find a shortest tour that comes within a distance of…

Data Structures and Algorithms · Computer Science 2025-02-27 Fabian Frei , Ahmed Ghazy , Tim A. Hartmann , Florian Hörsch , Dániel Marx

The presented work addresses two-stage stochastic programs (2SPs), a broadly applicable model to capture optimization problems subject to uncertain parameters with adjustable decision variables. In case the adjustable or second-stage…

Optimization and Control · Mathematics 2023-07-21 Jan Kronqvist , Boda Li , Jan Rolfes , Shudian Zhao

We show improved approximation guarantees for the traveling salesman problem on cubic graphs, and cubic bipartite graphs. For cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi (2014) by giving a simple…

Data Structures and Algorithms · Computer Science 2016-06-27 Anke van Zuylen

We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…

Computational Complexity · Computer Science 2008-09-02 Piotr Berman , Bhaskar DasGupta , Marek Karpinski

In the Strip Packing problem (SP), we are given a vertical half-strip $[0,W]\times[0,\infty)$ and a set of $n$ axis-aligned rectangles of width at most $W$. The goal is to find a non-overlapping packing of all rectangles into the strip such…

Data Structures and Algorithms · Computer Science 2022-05-09 Arindam Khan , Aditya Lonkar , Arnab Maiti , Amatya Sharma , Andreas Wiese

We consider the problem of approximating a multiple-input multiple-output (MIMO) $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hat H(s)$ of much smaller degree, so that the…

Optimization and Control · Mathematics 2008-07-31 Paul Van Dooren , Kyle A. Gallivan , P. -A. Absil

We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly…

Computer Science and Game Theory · Computer Science 2017-07-24 S. Roch , P. Marcotte , G. Savard

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…

Computational Complexity · Computer Science 2017-05-15 Sören Henning , Klaus Jansen , Malin Rau , Lars Schmarje

In the Stackelberg Network Pricing problem, one has to assign tariffs to a certain subset of the arcs of a given transportation network. The aim is to maximize the amount paid by the user of the network, knowing that the user will take a…

Data Structures and Algorithms · Computer Science 2011-03-07 Gwenaël Joret

The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs $\varepsilon \subseteq E$ or vertices $\nu \subseteq V$ whose removal $G\setminus \varepsilon$, $G\setminus \nu$…

Discrete Mathematics · Computer Science 2025-04-18 Michael Hecht , Krzysztof Gonciarz , Szabolcs Horvát

We study the problem of finding a tour of $n$ points in which every edge is long. More precisely, we wish to find a tour that visits every point exactly once, maximizing the length of the shortest edge in the tour. The problem is known as…

Data Structures and Algorithms · Computer Science 2016-06-29 László Kozma , Tobias Mömke

The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) comprises three sets of agents, namely students, projects and lecturers, where students have preferences over projects and lecturers have preferences…

Data Structures and Algorithms · Computer Science 2020-09-08 Frances Cooper , David Manlove

We study the maximum constraint satisfaction problem, Max-CSP, in the streaming setting. Given $n$ variables, the constraints arrive sequentially in an arbitrary order, with each constraint involving only a small subset of the variables.…

Data Structures and Algorithms · Computer Science 2026-04-03 Amir Azarmehr , Soheil Behnezhad , Shane Ferrante

Ride-pooling, which accommodates multiple passenger requests in a single trip, has the potential to significantly increase fleet utilization in shared mobility platforms. The ride-pooling assignment problem finds optimal co-riders to…

Optimization and Control · Mathematics 2022-04-15 Qi Luo , Viswanath Nagarajan , Alexander Sundt , Yafeng Yin , John Vincent , Mehrdad Shahabi

We provide a polynomial time 4/3 approximation algorithm for TSP on metrics arising from the metric completion of cubic 3-edge connected graphs.

Data Structures and Algorithms · Computer Science 2011-01-31 Nishita Aggarwal , Naveen Garg , Swati Gupta

In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…

Data Structures and Algorithms · Computer Science 2026-01-06 Radek Hušek , Dušan Knop , Tomáš Masařík

The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…

Data Structures and Algorithms · Computer Science 2025-11-10 Ce Jin , Yael Kirkpatrick , Michał Stawarz , Virginia Vassilevska Williams