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DOI: 10.4230/OASIcs.ATMOS.2024.7

Improved Algorithms for the Capacitated Team Orienteering Problem

Authors: Gianlorenzo D'Angelo, Mattia D'Emidio, Esmaeil Delfaraz, and Gabriele Di Stefano

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

Abstract

We study the Capacitated Team Orienteering Problem, where a fleet of vehicles with capacities have to meet customers with known demands and prizes for a single commodity. The objective is to maximize the total prize and to assign a sequence of customers to each vehicle while keeping the total distance traveled within a given budget and such that the total demand served by each vehicle does not exceed its capacity. The problem has been widely studied both from a theoretical and a practical point of view. The contribution of this paper is twofold: (1) We advance the theoretical knowledge on the problem by providing new approximation algorithms that achieve, under some natural assumption, improved approximation ratios compared to the current best algorithms; (2) We propose four efficient heuristics that outperform the current state-of-the-art practical methods in the sense that they compute solutions that collect nearly the same prize in a significantly smaller running time. We also experimentally test the scalability of the new heuristics, showing that their running time increases approximately linearly with the size of the input, allowing us to process large graphs which were not possible to analyze before.

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Gianlorenzo D'Angelo, Mattia D'Emidio, Esmaeil Delfaraz, and Gabriele Di Stefano. Improved Algorithms for the Capacitated Team Orienteering Problem. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dangelo_et_al:OASIcs.ATMOS.2024.7,
  author =	{D'Angelo, Gianlorenzo and D'Emidio, Mattia and Delfaraz, Esmaeil and Di Stefano, Gabriele},
  title =	{{Improved Algorithms for the Capacitated Team Orienteering Problem}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{7:1--7:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.7},
  URN =		{urn:nbn:de:0030-drops-211957},
  doi =		{10.4230/OASIcs.ATMOS.2024.7},
  annote =	{Keywords: Vehicle Routing, Approximation algorithms, Algorithm Engineering}
}

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DOI: 10.4230/LIPIcs.ISAAC.2022.9

Budgeted Out-Tree Maximization with Submodular Prizes

Authors: Gianlorenzo D'Angelo, Esmaeil Delfaraz, and Hugo Gilbert

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract

We consider a variant of the prize collecting Steiner tree problem in which we are given a directed graph D = (V,A), a monotone submodular prize function p:2^V → ℝ^+ ∪ {0}, a cost function c:V → ℤ^+, a root vertex r ∈ V, and a budget B. The aim is to find an out-subtree T of D rooted at r that costs at most B and maximizes the prize function. We call this problem Directed Rooted Submodular Tree (DRST). For the case of undirected graphs and additive prize functions, Moss and Rabani [SIAM J. Comput. 2007] gave an algorithm that guarantees an O(log|V|)-approximation factor if a violation by a factor 2 of the budget constraint is allowed. Bateni et al. [SIAM J. Comput. 2018] improved the budget violation factor to 1+ε at the cost of an additional approximation factor of O(1/ε²), for any ε ∈ (0,1]. For directed graphs, Ghuge and Nagarajan [SODA 2020] gave an optimal quasi-polynomial time O({log n'}/{log log n'})-approximation algorithm, where n' is the number of vertices in an optimal solution, for the case in which the costs are associated to the edges. In this paper, we give a polynomial time algorithm for DRST that guarantees an approximation factor of O(√B/ε³) at the cost of a budget violation of a factor 1+ε, for any ε ∈ (0,1]. The same result holds for the edge-cost case, to the best of our knowledge this is the first polynomial time approximation algorithm for this case. We further show that the unrooted version of DRST can be approximated to a factor of O(√B) without budget violation, which is an improvement over the factor O(Δ √B) given in [Kuo et al. IEEE/ACM Trans. Netw. 2015] for the undirected and unrooted case, where Δ is the maximum degree of the graph. Finally, we provide some new/improved approximation bounds for several related problems, including the additive-prize version of DRST, the maximum budgeted connected set cover problem, and the budgeted sensor cover problem.

Cite as

Gianlorenzo D'Angelo, Esmaeil Delfaraz, and Hugo Gilbert. Budgeted Out-Tree Maximization with Submodular Prizes. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dangelo_et_al:LIPIcs.ISAAC.2022.9,
  author =	{D'Angelo, Gianlorenzo and Delfaraz, Esmaeil and Gilbert, Hugo},
  title =	{{Budgeted Out-Tree Maximization with Submodular Prizes}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.9},
  URN =		{urn:nbn:de:0030-drops-172945},
  doi =		{10.4230/LIPIcs.ISAAC.2022.9},
  annote =	{Keywords: Prize Collecting Steiner Tree, Directed graphs, Approximation Algorithms, Budgeted Problem}
}

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Documents authored by Delfaraz, Esmaeil

Improved Algorithms for the Capacitated Team Orienteering Problem

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Budgeted Out-Tree Maximization with Submodular Prizes

Abstract

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