9 Search Results for "Fukunaga, Takuro"

Document
DOI: 10.4230/LIPIcs.DISC.2025.7
On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits

Authors: Matthias Artmann, Andreas Padalkin, and Christian Scheideler

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In programmable matter, we consider a large number of tiny, primitive computational entities called particles that run distributed algorithms to control global properties of the particle structure. Shape formation problems, where the particles have to reorganize themselves into a desired shape using basic movement abilities, are particularly interesting. In the related shape containment problem, the particles are given the description of a shape S and have to find maximally scaled representations of S within the initial configuration, without movements. For example, if S is a triangle, they have to identify the largest subsets of particles that already form a triangle. While the shape formation problem is being studied extensively, no attention has been given to the shape containment problem, which may have additional uses besides shape formation, such as detecting structural flaws. In this paper, we consider the shape containment problem within the geometric amoebot model for programmable matter, using its reconfigurable circuit extension to enable the instantaneous transmission of primitive signals on connected subsets of particles. We first prove a lower runtime bound of Ω (√n) synchronous rounds for the general problem, where n is the number of particles. Then, we present simple and efficient primitives for identifying subsets that form the desired shape. Using these primitives, we construct a large class of shapes which we call snowflakes. This class contains, among others, all shapes composed of parallelograms and hexagons, and the class of star convex shapes. Let k be the maximum scale of the considered shape in a given amoebot structure. If the shape is star convex, we solve it within 𝒪 (log² k) rounds. If it is a snowflake but not star convex, we solve it within 𝒪 (√n log n) rounds.
Cite as

Matthias Artmann, Andreas Padalkin, and Christian Scheideler. On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{artmann_et_al:LIPIcs.DISC.2025.7,
  author =	{Artmann, Matthias and Padalkin, Andreas and Scheideler, Christian},
  title =	{{On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.7},
  URN =		{urn:nbn:de:0030-drops-248240},
  doi =		{10.4230/LIPIcs.DISC.2025.7},
  annote =	{Keywords: Programmable matter, amoebot model, reconfigurable circuits, shape containment}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.92
Incremental Maximization for a Broad Class of Objectives

Authors: Yann Disser and David Weckbecker

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider incremental maximization problems, where the solution has to be built up gradually by adding elements one after the other. In every step, the incremental solution must be competitive, compared against the optimum solution of the current cardinality. We prove that a competitive solution always exists when the objective function is monotone and β-accountable, by providing a scaling algorithm that guarantees a constant competitive ratio. This generalizes known results and, importantly, yields the first competitive algorithm for the natural class of monotone and subadditive objective functions.
Cite as

Yann Disser and David Weckbecker. Incremental Maximization for a Broad Class of Objectives. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 92:1-92:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{disser_et_al:LIPIcs.ESA.2025.92,
  author =	{Disser, Yann and Weckbecker, David},
  title =	{{Incremental Maximization for a Broad Class of Objectives}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{92:1--92:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.92},
  URN =		{urn:nbn:de:0030-drops-245613},
  doi =		{10.4230/LIPIcs.ESA.2025.92},
  annote =	{Keywords: incremental maximization, competitive analysis, subadditive functions}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.4
Streaming Algorithms for Network Design

Authors: Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph G = (V, E) and an integer connectivity requirement r(uv) for each u, v ∈ V. The objective is to find a minimum-weight subgraph H ⊆ G such that, for every pair of vertices u, v ∈ V, u and v are r(uv)-edge/vertex-connected. Recent work by [Ce Jin et al., 2024] obtained approximation algorithms for edge-connectivity augmentation, and via that, also derived algorithms for edge-connectivity SNDP (EC-SNDP). In this work we consider vertex-connectivity setting (VC-SNDP) and obtain several results for it as well as improved results for EC-SNDP. - We provide a general framework for solving connectivity problems including SNDP and others in streaming; this is based on a connection to fault-tolerant spanners. For VC-SNDP we provide an O(tk)-approximation in Õ(k^{1-1/t}n^{1 + 1/t}) space, where k is the maximum connectivity requirement, assuming an exact algorithm at the end of the stream. Using a refined LP-based analysis, we provide an O(β t)-approximation where β is the integrality gap of the natural cut-based LP relaxation. These are the first approximation algorithms in the streaming model for VC-SNDP. When applied to the EC-SNDP, our framework provides an O(t)-approximation in Õ(k^{1/2-1/(2t)}n^{1 + 1/t} + kn) space, improving the O(t log k)-approximation of [Ce Jin et al., 2024] using Õ(kn^{1+1/t}) space; this also extends to element-connectivity SNDP. - We consider vertex connectivity-augmentation in the link-arrival model. The input is a k-vertex-connected spanning subgraph G, and additional weighted links L arrive in the stream; the goal is to store the min-weight set of links such that G ∪ L is (k+1)-vertex-connected. We obtain constant-factor approximations in near-linear space for k = 1, 2. Our result for k = 2 is based on using the SPQR tree, a novel application for this well-known representation of 2-connected graphs.
Cite as

Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian. Streaming Algorithms for Network Design. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chekuri_et_al:LIPIcs.APPROX/RANDOM.2025.4,
  author =	{Chekuri, Chandra and Jain, Rhea and Mahabadi, Sepideh and Vakilian, Ali},
  title =	{{Streaming Algorithms for Network Design}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  URN =		{urn:nbn:de:0030-drops-243709},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  annote =	{Keywords: Streaming Algorithms, Survivable Network Design, Fault-Tolerant Spanners}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.18
A Randomized Rounding Approach for DAG Edge Deletion

Authors: Sina Kalantarzadeh, Nathan Klein, and Victor Reis

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In the DAG Edge Deletion problem, we are given an edge-weighted directed acyclic graph and a parameter k, and the goal is to delete the minimum weight set of edges so that the resulting graph has no paths of length k. This problem, which has applications to scheduling, was introduced in 2015 by Kenkre, Pandit, Purohit, and Saket. They gave a k-approximation and showed that it is UGC-Hard to approximate better than ⌊0.5k⌋ for any constant k ≥ 4 using a work of Svensson from 2012. The approximation ratio was improved to 2/3(k+1) by Klein and Wexler in 2016. In this work, we introduce a randomized rounding framework based on distributions over vertex labels in [0,1]. The most natural distribution is to sample labels independently from the uniform distribution over [0,1]. We show this leads to a (2-√2)(k+1) ≈ 0.585(k+1)-approximation. By using a modified (but still independent) label distribution, we obtain a 0.549(k+1)-approximation for the problem, as well as show that no independent distribution over labels can improve our analysis to below 0.542(k+1). Finally, we show a 0.5(k+1)-approximation for bipartite graphs and for instances with structured LP solutions. Whether this ratio can be obtained in general is open.
Cite as

Sina Kalantarzadeh, Nathan Klein, and Victor Reis. A Randomized Rounding Approach for DAG Edge Deletion. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kalantarzadeh_et_al:LIPIcs.APPROX/RANDOM.2025.18,
  author =	{Kalantarzadeh, Sina and Klein, Nathan and Reis, Victor},
  title =	{{A Randomized Rounding Approach for DAG Edge Deletion}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  URN =		{urn:nbn:de:0030-drops-243840},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  annote =	{Keywords: Approximation Algorithms, Randomized Algorithms, Linear Programming, Graph Algorithms, Scheduling}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.128
3.415-Approximation for Coflow Scheduling via Iterated Rounding

Authors: Lars Rohwedder and Leander Schnaars

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We provide an algorithm giving a 140/41 (< 3.415)-approximation for Coflow Scheduling and a 4.36-approximation for Coflow Scheduling with release dates. This improves upon the best known 4- and respectively 5-approximations and addresses an open question posed by Agarwal, Rajakrishnan, Narayan, Agarwal, Shmoys, and Vahdat [Agarwal et al., 2018], Fukunaga [Fukunaga, 2022], and others. We additionally show that in an asymptotic setting, the algorithm achieves a (2+ε)-approximation, which is essentially optimal under ℙ ≠ NP. The improvements are achieved using a novel edge allocation scheme using iterated LP rounding together with a framework which enables establishing strong bounds for combinations of several edge allocation algorithms.
Cite as

Lars Rohwedder and Leander Schnaars. 3.415-Approximation for Coflow Scheduling via Iterated Rounding. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 128:1-128:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder_et_al:LIPIcs.ICALP.2025.128,
  author =	{Rohwedder, Lars and Schnaars, Leander},
  title =	{{3.415-Approximation for Coflow Scheduling via Iterated Rounding}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{128:1--128:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.128},
  URN =		{urn:nbn:de:0030-drops-235050},
  doi =		{10.4230/LIPIcs.ICALP.2025.128},
  annote =	{Keywords: Coflow Scheduling, Approximation Algorithms, Iterated Rounding}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.14
Multivariate Exploration of Metric Dilation

Authors: Aritra Banik, Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Satyabrata Jana, and Saket Saurabh

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Let G be a weighted graph embedded in a metric space (M, d_M). The vertices of G correspond to the points in M, with the weight of each edge uv being the distance d_M(u,v) between their respective points in M. The dilation (or stretch) of G is defined as the minimum factor t such that, for any pair of vertices u,v, the distance between u and v - represented by the weight of a shortest u,v-path - is at most t⋅ d_M(u,v). We study Dilation t-Augmentation, where the objective is, given a metric M, a graph G, and numerical values k and t, to determine whether G can be transformed into a graph with dilation t by adding at most k edges. Our primary focus is on the scenario where the metric M is the shortest path metric of an unweighted graph Γ. Even in this specific case, Dilation t-Augmentation remains computationally challenging. In particular, the problem is W[2]-hard parameterized by k when Γ is a complete graph, already for t = 2. Our main contribution lies in providing new insights into the impact of combinations of various parameters on the computational complexity of the problem. We establish the following. - The parameterized dichotomy of the problem with respect to dilation t, when the graph G is sparse: Parameterized by k, the problem is FPT for graphs excluding a biclique K_{d,d} as a subgraph for t ≤ 2 and the problem is W[1]-hard for t ≥ 3 even if G is a forest consisting of disjoint stars. - The problem is FPT parameterized by the combined parameter k+t+Δ, where Δ is the maximum degree of the graph G or Γ.
Cite as

Aritra Banik, Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Satyabrata Jana, and Saket Saurabh. Multivariate Exploration of Metric Dilation. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banik_et_al:LIPIcs.STACS.2025.14,
  author =	{Banik, Aritra and Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Jana, Satyabrata and Saurabh, Saket},
  title =	{{Multivariate Exploration of Metric Dilation}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.14},
  URN =		{urn:nbn:de:0030-drops-228395},
  doi =		{10.4230/LIPIcs.STACS.2025.14},
  annote =	{Keywords: Metric dilation, geometric spanner, fixed-parameter tractability}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.36
Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling

Authors: Takuro Fukunaga

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
Coflow is a set of related parallel data flows in a network. The goal of the coflow scheduling is to process all the demands of the given coflows while minimizing the weighted completion time. It is known that the coflow scheduling problem admits several polynomial-time 5-approximation algorithms that compute solutions by rounding linear programming (LP) relaxations of the problem. In this paper, we investigate the time-indexed LP relaxation for coflow scheduling. We show that the integrality gap of the time-indexed LP relaxation is at most 4. We also show that yet another polynomial-time 5-approximation algorithm can be obtained by rounding the solutions to the time-indexed LP relaxation.
Cite as

Takuro Fukunaga. Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fukunaga:LIPIcs.APPROX/RANDOM.2022.36,
  author =	{Fukunaga, Takuro},
  title =	{{Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.36},
  URN =		{urn:nbn:de:0030-drops-171581},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.36},
  annote =	{Keywords: coflow scheduling, hypergraph matching, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.316
Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation

Authors: Takuro Fukunaga

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A major contribution of this paper is the development of a strongly polynomial-time 4/3-approximation algorithm for the problem. Specifically, we show that a linear programming relaxation of the problem is half-integral, and that the half-integral optimal solution can be rounded to a 4/3-approximate solution. We also prove that the linear programming relaxation of the problem with the edge-connectivity constraints is equivalent to minimizing the cost of half-integral multiflows that satisfy flow demands given from terminals. This observation implies a strongly polynomial-time algorithm for computing a minimum cost half-integral multiflow under flow demand constraints.
Cite as

Takuro Fukunaga. Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 316-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{fukunaga:LIPIcs.STACS.2015.316,
  author =	{Fukunaga, Takuro},
  title =	{{Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{316--328},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.316},
  URN =		{urn:nbn:de:0030-drops-49236},
  doi =		{10.4230/LIPIcs.STACS.2015.316},
  annote =	{Keywords: survivable network design, multiflow, LP rounding}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.209
Deliver or hold: Approximation Algorithms for the Periodic Inventory Routing Problem

Authors: Takuro Fukunaga, Afshin Nikzad, and R. Ravi

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
The inventory routing problem involves trading off inventory holding costs at client locations with vehicle routing costs to deliver frequently from a single central depot to meet deterministic client demands over a finite planing horizon. In this paper, we consider periodic solutions that visit clients in one of several specified frequencies, and focus on the case when the frequencies of visiting nodes are nested. We give the first constant-factor approximation algorithms for designing optimum nested periodic schedules for the problem with no limit on vehicle capacities by simple reductions to prize-collecting network design problems. For instance, we present a 2.55-approximation algorithm for the minimum-cost nested periodic schedule where the vehicle routes are modeled as minimum Steiner trees. We also show a general reduction from the capacitated problem where all vehicles have the same capacity to the uncapacitated version with a slight loss in performance. This reduction gives a 4.55-approximation for the capacitated problem. In addition, we prove several structural results relating the values of optimal policies of various types.
Cite as

Takuro Fukunaga, Afshin Nikzad, and R. Ravi. Deliver or hold: Approximation Algorithms for the Periodic Inventory Routing Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 209-225, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{fukunaga_et_al:LIPIcs.APPROX-RANDOM.2014.209,
  author =	{Fukunaga, Takuro and Nikzad, Afshin and Ravi, R.},
  title =	{{Deliver or hold: Approximation Algorithms for the Periodic Inventory Routing Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{209--225},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.209},
  URN =		{urn:nbn:de:0030-drops-46985},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.209},
  annote =	{Keywords: Inventry Routing Problem, Approximation algorithm, Prize-collecting Steiner Tree}
}
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