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Related papers: Combinatorial Algorithms for Rooted Prize-Collecti…

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Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop vertices from the tour at the cost of vertex-dependent penalties. The quality of a solution is then measured by adding the length of the tour and the…

Data Structures and Algorithms · Computer Science 2025-01-14 Jannis Blauth , Nathan Klein , Martin Nägele

We introduce and study the Marco Polo problem, which is a combinatorial approach to geometric localization. In this problem, we are told there are one or more points of interest (POIs) within distance $n$ of the origin that we wish to…

Computational Geometry · Computer Science 2025-08-21 Ofek Gila , Michael T. Goodrich , Zahra Hadizadeh , Daniel S. Hirschberg , Shayan Taherijam

We study the problem of finding a minimum weight connected subgraph spanning at least $k$ vertices on planar, node-weighted graphs. We give a $(4+\eps)$-approximation algorithm for this problem. We achieve this by utilizing the recent LMP…

Data Structures and Algorithms · Computer Science 2018-05-09 Jarosław Byrka , Mateusz Lewandowski , Joachim Spoerhase

Constrained forest problems form a class of graph problems where specific connectivity requirements for certain cuts within the graph must be satisfied by selecting the minimum-cost set of edges. The prize-collecting version of these…

Data Structures and Algorithms · Computer Science 2025-04-23 Ali Ahmadi , Iman Gholami , MohammadTaghi Hajiaghayi , Peyman Jabbarzade , Mohammad Mahdavi

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

Machine Learning · Computer Science 2026-03-05 Henri Schmidt , Peter Halmos , Ben Raphael

We propose a new model for formalizing reward collection problems on graphs with dynamically generated rewards which may appear and disappear based on a stochastic model. The *robot routing problem* is modeled as a graph whose nodes are…

Systems and Control · Computer Science 2017-07-18 Rayna Dimitrova , Ivan Gavran , Rupak Majumdar , Vinayak S. Prabhu , Sadegh Esmaeil Zadeh Soudjani

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…

Data Structures and Algorithms · Computer Science 2013-09-03 Kameng Nip , Zhenbo Wang , Wenxun Xing

In linear combinatorial optimization, we aim to find $S^* = \arg\min_{S \in \mathcal{F}} \langle w,\mathbf{1}_S \rangle$ for a family $\mathcal{F} \subseteq 2^U$ over a ground set $U$ of $n$ elements. Traditionally, $w$ is known or…

The Team Orienteering Problem (TOP) is an NP-hard routing problem in which a fleet of identical vehicles aims at collecting rewards (prizes) available at given locations, while satisfying restrictions on the travel times. In TOP, each…

Data Structures and Algorithms · Computer Science 2020-01-06 Lucas Assunção , Geraldo Robson Mateus

Text-to-image generation models have achieved remarkable progress in preference optimization, yet achieving robust alignment across diverse reward models remains a significant challenge. Existing multi-reward fusion approaches rely on…

Computer Vision and Pattern Recognition · Computer Science 2026-05-14 Ying Ba , Tianyu Zhang , Mohan Zhou , Yalong Bai , Wenyi Mo , Guiwei Zhang , Bing Su , Ji-Rong Wen

This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained problems and problems with non-binary variables. The algorithm returns optimal…

Quantum Physics · Physics 2024-08-14 Tavis Bennett , Lyle Noakes , Jingbo B. Wang

Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…

Data Structures and Algorithms · Computer Science 2021-12-16 Tesshu Hanaka , Yasuaki Kobayashi , Kazuhiro Kurita , See Woo Lee , Yota Otachi

In the Connected Budgeted maximum Coverage problem (CBC), we are given a collection of subsets $\mathcal{S}$, defined over a ground set $X$, and an undirected graph $G=(V,E)$, where each node is associated with a set of $\mathcal{S}$. Each…

Data Structures and Algorithms · Computer Science 2025-04-11 Gianlorenzo D'Angelo , Esmaeil Delfaraz

This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is…

Artificial Intelligence · Computer Science 2023-12-29 Luciano E. Almeida , Douglas G. Macharet

We propose a novel non-linear extension to the Orienteering Problem (OP), called the Correlated Orienteering Problem (COP). We use COP to model the planning of informative tours for the persistent monitoring of a spatiotemporal field with…

Robotics · Computer Science 2014-12-16 Jingjin Yu , Mac Schwager , Daniela Rus

Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…

Performance · Computer Science 2024-01-10 Wenkai Dai , Michael Dinitz , Klaus-Tycho Foerster , Long Luo , Stefan Schmid

The enumeration of quarter-plane lattice walks with small steps is a classical problem in combinatorics. An effective approach is the kernel method, where the solution is derived by positive term extraction. Alternatively, one may reduce…

Combinatorics · Mathematics 2025-05-12 Ruijie Xu

Graph routing problems have been investigated extensively in operations research, computer science and engineering due to their ubiquity and vast applications. In this paper, we study constant approximation algorithms for some variations of…

Data Structures and Algorithms · Computer Science 2020-06-24 Xiaoyan Zhang , Donglei Du , Gregory Gutin , Qiaoxia Ming , Jian Sun

We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…