77 Search Results for "Mathieu, Claire"

Volume

LIPIcs, Volume 60

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

APPROX/RANDOM 2016, September 7-9, 2016, Paris, France

Editors: Klaus Jansen, Claire Mathieu, José D. P. Rolim, and Chris Umans

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.8
Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects

Authors: Pritam Acharya, Sujoy Bhore, Aaryan Gupta, Arindam Khan, Bratin Mondal, and Andreas Wiese

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study the geometric knapsack problem in which we are given a set of d-dimensional objects (each with associated profits) and the goal is to find the maximum profit subset that can be packed non-overlappingly into a given d-dimensional (unit hypercube) knapsack. Even if d = 2 and all input objects are disks, this problem is known to be NP-hard [Demaine, Fekete, Lang, 2010]. In this paper, we give polynomial time (1+ε)-approximation algorithms for the following types of input objects in any constant dimension d: - disks and hyperspheres, - a class of fat convex polygons that generalizes regular k-gons for k ≥ 5 (formally, polygons with a constant number of edges, whose lengths are in a bounded range, and in which each angle is strictly larger than π/2), - arbitrary fat convex objects that are sufficiently small compared to the knapsack. We remark that in our PTAS for disks and hyperspheres, we output the computed set of objects, but for a O_ε(1) of them we determine their coordinates only up to an exponentially small error. However, it is not clear whether there always exists a (1+ε)-approximate solution that uses only rational coordinates for the disks' centers. We leave this as an open problem which is related to well-studied geometric questions in the realm of circle packing.
Cite as

Pritam Acharya, Sujoy Bhore, Aaryan Gupta, Arindam Khan, Bratin Mondal, and Andreas Wiese. Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{acharya_et_al:LIPIcs.ICALP.2024.8,
  author =	{Acharya, Pritam and Bhore, Sujoy and Gupta, Aaryan and Khan, Arindam and Mondal, Bratin and Wiese, Andreas},
  title =	{{Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.8},
  URN =		{urn:nbn:de:0030-drops-201511},
  doi =		{10.4230/LIPIcs.ICALP.2024.8},
  annote =	{Keywords: Approximation Algorithms, Polygon Packing, Circle Packing, Sphere Packing, Geometric Knapsack, Resource Augmentation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.18
It’s Hard to HAC Average Linkage!

Authors: MohammadHossein Bateni, Laxman Dhulipala, Kishen N. Gowda, D. Ellis Hershkowitz, Rajesh Jayaram, and Jakub Łącki

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Average linkage Hierarchical Agglomerative Clustering (HAC) is an extensively studied and applied method for hierarchical clustering. Recent applications to massive datasets have driven significant interest in near-linear-time and efficient parallel algorithms for average linkage HAC. We provide hardness results that rule out such algorithms. On the sequential side, we establish a runtime lower bound of n^{3/2-ε} on n node graphs for sequential combinatorial algorithms under standard fine-grained complexity assumptions. This essentially matches the best-known running time for average linkage HAC. On the parallel side, we prove that average linkage HAC likely cannot be parallelized even on simple graphs by showing that it is CC-hard on trees of diameter 4. On the possibility side, we demonstrate that average linkage HAC can be efficiently parallelized (i.e., it is in NC) on paths and can be solved in near-linear time when the height of the output cluster hierarchy is small.
Cite as

MohammadHossein Bateni, Laxman Dhulipala, Kishen N. Gowda, D. Ellis Hershkowitz, Rajesh Jayaram, and Jakub Łącki. It’s Hard to HAC Average Linkage!. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bateni_et_al:LIPIcs.ICALP.2024.18,
  author =	{Bateni, MohammadHossein and Dhulipala, Laxman and Gowda, Kishen N. and Hershkowitz, D. Ellis and Jayaram, Rajesh and {\L}\k{a}cki, Jakub},
  title =	{{It’s Hard to HAC Average Linkage!}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.18},
  URN =		{urn:nbn:de:0030-drops-201613},
  doi =		{10.4230/LIPIcs.ICALP.2024.18},
  annote =	{Keywords: Clustering, Hierarchical Graph Clustering, HAC, Fine-Grained Complexity, Parallel Algorithms, CC}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.35
A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs

Authors: Charlie Carlson, Ewan Davies, Alexandra Kolla, and Aditya Potukuchi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph - in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs. Efficient counting algorithms typically apply to "high-temperature" problems on bounded-degree graphs, and our contribution is a notable exception as it applies to dense graphs in a low-temperature setting. Our methods give a counting-focused complement to the long line of work in combinatorial optimization showing that CSPs such as Max-Cut and Unique Games are easy on dense graphs via spectral arguments. Our contributions include a novel extension of the method of graph containers that differs considerably from other recent low-temperature algorithms. The additional key insights come from spectral graph theory and have previously been successful in approximation algorithms. As a result, we can overcome some limitations that seem inherent to the aforementioned class of algorithms. In particular, we exploit the fact that dense, regular graphs exhibit a kind of small-set expansion (i.e., bounded threshold rank), which, via subspace enumeration, lets us enumerate small cuts efficiently.
Cite as

Charlie Carlson, Ewan Davies, Alexandra Kolla, and Aditya Potukuchi. A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 35:1-35:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{carlson_et_al:LIPIcs.ICALP.2024.35,
  author =	{Carlson, Charlie and Davies, Ewan and Kolla, Alexandra and Potukuchi, Aditya},
  title =	{{A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{35:1--35:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.35},
  URN =		{urn:nbn:de:0030-drops-201782},
  doi =		{10.4230/LIPIcs.ICALP.2024.35},
  annote =	{Keywords: approximate counting, independent sets, bipartite graphs, graph containers}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.61
Parameterized Algorithms for Steiner Forest in Bounded Width Graphs

Authors: Andreas Emil Feldmann and Michael Lampis

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in several graph classes of bounded width. The problem takes an edge-weighted graph and pairs of vertices as input, and the aim is to find a minimum cost subgraph in which each given vertex pair lies in the same connected component. It is known that this problem is APX-hard in general, and NP-hard on graphs of treewidth 3, treedepth 4, and feedback vertex set size 2. However, Bateni, Hajiaghayi and Marx [JACM, 2011] gave an approximation scheme with a runtime of n^O(k²/ε) on graphs of treewidth k. Our main result is a much faster efficient parameterized approximation scheme (EPAS) with a runtime of 2^O(k²/ε log k/ε)⋅n^O(1). If k instead is the vertex cover number of the input graph, we show how to compute the optimum solution in 2^O(k log k)⋅n^O(1) time, and we also prove that this runtime dependence on k is asymptotically best possible, under ETH. Furthermore, if k is the size of a feedback edge set, then we obtain a faster 2^O(k)⋅n^O(1) time algorithm, which again cannot be improved under ETH.
Cite as

Andreas Emil Feldmann and Michael Lampis. Parameterized Algorithms for Steiner Forest in Bounded Width Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 61:1-61:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{feldmann_et_al:LIPIcs.ICALP.2024.61,
  author =	{Feldmann, Andreas Emil and Lampis, Michael},
  title =	{{Parameterized Algorithms for Steiner Forest in Bounded Width Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{61:1--61:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.61},
  URN =		{urn:nbn:de:0030-drops-202048},
  doi =		{10.4230/LIPIcs.ICALP.2024.61},
  annote =	{Keywords: Steiner Forest, Approximation Algorithms, FPT algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.93
Streaming Algorithms for Connectivity Augmentation

Authors: Ce Jin, Michael Kapralov, Sepideh Mahabadi, and Ali Vakilian

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study the k-connectivity augmentation problem (k-CAP) in the single-pass streaming model. Given a (k-1)-edge connected graph G = (V,E) that is stored in memory, and a stream of weighted edges (also called links) L with weights in {0,1,… ,W}, the goal is to choose a minimum weight subset L' ⊆ L of the links such that G' = (V,E∪ L') is k-edge connected. We give a (2+ε)-approximation algorithm for this problem which requires to store O(ε^{-1} nlog n) words. Moreover, we show the tightness of our result: Any algorithm with better than 2-approximation for the problem requires Ω(n²) bits of space even when k = 2. This establishes a gap between the optimal approximation factor one can obtain in the streaming vs the offline setting for k-CAP. We further consider a natural generalization to the fully streaming model where both E and L arrive in the stream in an arbitrary order. We show that this problem has a space lower bound that matches the best possible size of a spanner of the same approximation ratio. Following this, we give improved results for spanners on weighted graphs: We show a streaming algorithm that finds a (2t-1+ε)-approximate weighted spanner of size at most O(ε^{-1} n^{1+1/t}log n) for integer t, whereas the best prior streaming algorithm for spanner on weighted graphs had size depending on log W. We believe that this result is of independent interest. Using our spanner result, we provide an optimal O(t)-approximation for k-CAP in the fully streaming model with O(nk + n^{1+1/t}) words of space. Finally we apply our results to network design problems such as Steiner tree augmentation problem (STAP), k-edge connected spanning subgraph (k-ECSS) and the general Survivable Network Design problem (SNDP). In particular, we show a single-pass O(tlog k)-approximation for SNDP using O(kn^{1+1/t}) words of space, where k is the maximum connectivity requirement.
Cite as

Ce Jin, Michael Kapralov, Sepideh Mahabadi, and Ali Vakilian. Streaming Algorithms for Connectivity Augmentation. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 93:1-93:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{jin_et_al:LIPIcs.ICALP.2024.93,
  author =	{Jin, Ce and Kapralov, Michael and Mahabadi, Sepideh and Vakilian, Ali},
  title =	{{Streaming Algorithms for Connectivity Augmentation}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{93:1--93:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.93},
  URN =		{urn:nbn:de:0030-drops-202367},
  doi =		{10.4230/LIPIcs.ICALP.2024.93},
  annote =	{Keywords: streaming algorithms, connectivity augmentation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.122
An Improved Integrality Gap for Disjoint Cycles in Planar Graphs

Authors: Niklas Schlomberg

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We present a new greedy rounding algorithm for the Cycle Packing Problem for uncrossable cycle families in planar graphs. This improves the best-known upper bound for the integrality gap of the natural packing LP to a constant slightly less than 3.5. Furthermore, the analysis works for both edge- and vertex-disjoint packing. The previously best-known constants were 4 for edge-disjoint and 5 for vertex-disjoint cycle packing. This result also immediately yields an improved Erdős-Pósa ratio: for any uncrossable cycle family in a planar graph, the minimum number of vertices (edges) needed to hit all cycles in the family is less than 8.38 times the maximum number of vertex-disjoint (edge-disjoint, respectively) cycles in the family. Some uncrossable cycle families of interest to which the result can be applied are the family of all cycles in a directed or undirected graph, in undirected graphs also the family of all odd cycles and the family of all cycles containing exactly one edge from a specified set of demand edges. The last example is an equivalent formulation of the fully planar Disjoint Paths Problem. Here the Erdős-Pósa ratio translates to a ratio between integral multi-commodity flows and minimum cuts.
Cite as

Niklas Schlomberg. An Improved Integrality Gap for Disjoint Cycles in Planar Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 122:1-122:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{schlomberg:LIPIcs.ICALP.2024.122,
  author =	{Schlomberg, Niklas},
  title =	{{An Improved Integrality Gap for Disjoint Cycles in Planar Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{122:1--122:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.122},
  URN =		{urn:nbn:de:0030-drops-202651},
  doi =		{10.4230/LIPIcs.ICALP.2024.122},
  annote =	{Keywords: Cycle packing, planar graphs, disjoint paths}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.94
Parameterized Matroid-Constrained Maximum Coverage

Authors: François Sellier

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
In this paper, we introduce the concept of Density-Balanced Subset in a matroid, in which independent sets can be sampled so as to guarantee that (i) each element has the same probability to be sampled, and (ii) those events are negatively correlated. These Density-Balanced Subsets are subsets in the ground set of a matroid in which the traditional notion of uniform random sampling can be extended. We then provide an application of this concept to the Matroid-Constrained Maximum Coverage problem. In this problem, given a matroid ℳ = (V, ℐ) of rank k on a ground set V and a coverage function f on V, the goal is to find an independent set S ∈ ℐ maximizing f(S). This problem is an important special case of the much-studied submodular function maximization problem subject to a matroid constraint; this is also a generalization of the maximum k-cover problem in a graph. In this paper, assuming that the coverage function has a bounded frequency μ (i.e., any element of the underlying universe of the coverage function appears in at most μ sets), we design a procedure, parameterized by some integer ρ, to extract in polynomial time an approximate kernel of size ρ ⋅ k that is guaranteed to contain a 1 - (μ - 1)/ρ approximation of the optimal solution. This procedure can then be used to get a Fixed-Parameter Tractable Approximation Scheme (FPT-AS) providing a 1 - ε approximation in time (μ/ε)^O(k) ⋅ |V|^O(1). This generalizes and improves the results of [Manurangsi, 2019] and [Huang and Sellier, 2022], providing the first FPT-AS working on an arbitrary matroid. Moreover, as the kernel has a very simple characterization, it can be constructed in the streaming setting.
Cite as

François Sellier. Parameterized Matroid-Constrained Maximum Coverage. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 94:1-94:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{sellier:LIPIcs.ESA.2023.94,
  author =	{Sellier, Fran\c{c}ois},
  title =	{{Parameterized Matroid-Constrained Maximum Coverage}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{94:1--94:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.94},
  URN =		{urn:nbn:de:0030-drops-187475},
  doi =		{10.4230/LIPIcs.ESA.2023.94},
  annote =	{Keywords: Matroids, approximate kernel, maximum coverage}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.91
A Tight (1.5+ε)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees

Authors: Claire Mathieu and Hang Zhou

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
In the unsplittable capacitated vehicle routing problem (UCVRP) on trees, we are given a rooted tree with edge weights and a subset of vertices of the tree called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the root of the tree such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour does not exceed the capacity of 1. For the special case when all terminals have equal demands, a long line of research culminated in a quasi-polynomial time approximation scheme [Jayaprakash and Salavatipour, TALG 2023] and a polynomial time approximation scheme [Mathieu and Zhou, TALG 2023]. In this work, we study the general case when the terminals have arbitrary demands. Our main contribution is a polynomial time (1.5+ε)-approximation algorithm for the UCVRP on trees. This is the first improvement upon the 2-approximation algorithm more than 30 years ago. Our approximation ratio is essentially best possible, since it is NP-hard to approximate the UCVRP on trees to better than a 1.5 factor.
Cite as

Claire Mathieu and Hang Zhou. A Tight (1.5+ε)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 91:1-91:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{mathieu_et_al:LIPIcs.ICALP.2023.91,
  author =	{Mathieu, Claire and Zhou, Hang},
  title =	{{A Tight (1.5+\epsilon)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{91:1--91:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.91},
  URN =		{urn:nbn:de:0030-drops-181430},
  doi =		{10.4230/LIPIcs.ICALP.2023.91},
  annote =	{Keywords: approximation algorithms, capacitated vehicle routing, graph algorithms, combinatorial optimization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.27
An Approximation Algorithm for Distance-Constrained Vehicle Routing on Trees

Authors: Marc Dufay, Claire Mathieu, and Hang Zhou

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
In the Distance-constrained Vehicle Routing Problem (DVRP), we are given a graph with integer edge weights, a depot, a set of n terminals, and a distance constraint D. The goal is to find a minimum number of tours starting and ending at the depot such that those tours together cover all the terminals and the length of each tour is at most D. The DVRP on trees is of independent interest, because it is equivalent to the "virtual machine packing" problem on trees studied by Sindelar et al. [SPAA'11]. We design a simple and natural approximation algorithm for the tree DVRP, parameterized by ε > 0. We show that its approximation ratio is α + ε, where α ≈ 1.691, and in addition, that our analysis is essentially tight. The running time is polynomial in n and D. The approximation ratio improves on the ratio of 2 due to Nagarajan and Ravi [Networks'12]. The main novelty of this paper lies in the analysis of the algorithm. It relies on a reduction from the tree DVRP to the bounded space online bin packing problem via a new notion of "reduced length".
Cite as

Marc Dufay, Claire Mathieu, and Hang Zhou. An Approximation Algorithm for Distance-Constrained Vehicle Routing on Trees. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{dufay_et_al:LIPIcs.STACS.2023.27,
  author =	{Dufay, Marc and Mathieu, Claire and Zhou, Hang},
  title =	{{An Approximation Algorithm for Distance-Constrained Vehicle Routing on Trees}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.27},
  URN =		{urn:nbn:de:0030-drops-176794},
  doi =		{10.4230/LIPIcs.STACS.2023.27},
  annote =	{Keywords: vehicle routing, distance constraint, approximation algorithms, trees}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.63
Unsplittable Euclidean Capacitated Vehicle Routing: A (2+ε)-Approximation Algorithm

Authors: Fabrizio Grandoni, Claire Mathieu, and Hang Zhou

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
In the unsplittable capacitated vehicle routing problem, we are given a metric space with a vertex called depot and a set of vertices called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the depot such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour does not exceed the capacity of 1. Our main result is a polynomial-time (2+ε)-approximation algorithm for this problem in the two-dimensional Euclidean plane, i.e., for the special case where the terminals and the depot are associated with points in the Euclidean plane and their distances are defined accordingly. This improves on recent work by Blauth, Traub, and Vygen [IPCO'21] and Friggstad, Mousavi, Rahgoshay, and Salavatipour [IPCO'22].
Cite as

Fabrizio Grandoni, Claire Mathieu, and Hang Zhou. Unsplittable Euclidean Capacitated Vehicle Routing: A (2+ε)-Approximation Algorithm. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 63:1-63:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{grandoni_et_al:LIPIcs.ITCS.2023.63,
  author =	{Grandoni, Fabrizio and Mathieu, Claire and Zhou, Hang},
  title =	{{Unsplittable Euclidean Capacitated Vehicle Routing: A (2+\epsilon)-Approximation Algorithm}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{63:1--63:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.63},
  URN =		{urn:nbn:de:0030-drops-175660},
  doi =		{10.4230/LIPIcs.ITCS.2023.63},
  annote =	{Keywords: capacitated vehicle routing, approximation algorithms, Euclidean plane}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.68
Maximum Weight b-Matchings in Random-Order Streams

Authors: Chien-Chung Huang and François Sellier

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We consider the maximum weight b-matching problem in the random-order semi-streaming model. Assuming all weights are small integers drawn from [1,W], we present a 2 - 1/(2W) + ε approximation algorithm, using a memory of O(max(|M_G|, n) ⋅ poly(log(m),W,1/ε)), where |M_G| denotes the cardinality of the optimal matching. Our result generalizes that of Bernstein [Aaron Bernstein, 2020], which achieves a 3/2 + ε approximation for the maximum cardinality simple matching. When W is small, our result also improves upon that of Gamlath et al. [Gamlath et al., 2019], which obtains a 2 - δ approximation (for some small constant δ ∼ 10^{-17}) for the maximum weight simple matching. In particular, for the weighted b-matching problem, ours is the first result beating the approximation ratio of 2. Our technique hinges on a generalized weighted version of edge-degree constrained subgraphs, originally developed by Bernstein and Stein [Aaron Bernstein and Cliff Stein, 2015]. Such a subgraph has bounded vertex degree (hence uses only a small number of edges), and can be easily computed. The fact that it contains a 2 - 1/(2W) + ε approximation of the maximum weight matching is proved using the classical Kőnig-Egerváry’s duality theorem.
Cite as

Chien-Chung Huang and François Sellier. Maximum Weight b-Matchings in Random-Order Streams. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 68:1-68:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{huang_et_al:LIPIcs.ESA.2022.68,
  author =	{Huang, Chien-Chung and Sellier, Fran\c{c}ois},
  title =	{{Maximum Weight b-Matchings in Random-Order Streams}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{68:1--68:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.68},
  URN =		{urn:nbn:de:0030-drops-170062},
  doi =		{10.4230/LIPIcs.ESA.2022.68},
  annote =	{Keywords: Maximum weight matching, b-matching, streaming, random order}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.95
A PTAS for Capacitated Vehicle Routing on Trees

Authors: Claire Mathieu and Hang Zhou

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, for the entire range of the tour capacity. The result extends to the splittable CVRP.
Cite as

Claire Mathieu and Hang Zhou. A PTAS for Capacitated Vehicle Routing on Trees. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{mathieu_et_al:LIPIcs.ICALP.2022.95,
  author =	{Mathieu, Claire and Zhou, Hang},
  title =	{{A PTAS for Capacitated Vehicle Routing on Trees}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{95:1--95:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.95},
  URN =		{urn:nbn:de:0030-drops-164369},
  doi =		{10.4230/LIPIcs.ICALP.2022.95},
  annote =	{Keywords: approximation algorithms, capacitated vehicle routing, graph algorithms, combinatorial optimization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.43
Probabilistic Analysis of Euclidean Capacitated Vehicle Routing

Authors: Claire Mathieu and Hang Zhou

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We give a probabilistic analysis of the unit-demand Euclidean capacitated vehicle routing problem in the random setting, where the input distribution consists of n unit-demand customers modeled as independent, identically distributed uniform random points in the two-dimensional plane. The objective is to visit every customer using a set of routes of minimum total length, such that each route visits at most k customers, where k is the capacity of a vehicle. All of the following results are in the random setting and hold asymptotically almost surely. The best known polynomial-time approximation for this problem is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the ITP algorithm is near-optimal when k is either o(√n) or ω(√n), and they asked whether the ITP algorithm was "also effective in the intermediate range". In this work, we show that when k = √n, the ITP algorithm is at best a (1+c₀)-approximation for some positive constant c₀. On the other hand, the approximation ratio of the ITP algorithm was known to be at most 0.995+α due to Bompadre, Dror, and Orlin, where α is the approximation ratio of an algorithm for the traveling salesman problem. In this work, we improve the upper bound on the approximation ratio of the ITP algorithm to 0.915+α. Our analysis is based on a new lower bound on the optimal cost for the metric capacitated vehicle routing problem, which may be of independent interest.
Cite as

Claire Mathieu and Hang Zhou. Probabilistic Analysis of Euclidean Capacitated Vehicle Routing. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{mathieu_et_al:LIPIcs.ISAAC.2021.43,
  author =	{Mathieu, Claire and Zhou, Hang},
  title =	{{Probabilistic Analysis of Euclidean Capacitated Vehicle Routing}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.43},
  URN =		{urn:nbn:de:0030-drops-154769},
  doi =		{10.4230/LIPIcs.ISAAC.2021.43},
  annote =	{Keywords: capacitated vehicle routing, iterated tour partitioning, probabilistic analysis, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.68
A Simple Algorithm for Graph Reconstruction

Authors: Claire Mathieu and Hang Zhou

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
How efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a reconstruction algorithm based on multi-phase Voronoi-cell decomposition and using Õ(n^{3/2}) distance queries [Kannan et al., 2018]. In our work, we analyze a simple reconstruction algorithm. We show that, on random Δ-regular graphs, our algorithm uses Õ(n) distance queries. As by-products, we can reconstruct those graphs using O(log² n) queries to an all-distances oracle or Õ(n) queries to a betweenness oracle, and we bound the metric dimension of those graphs by log² n. Our reconstruction algorithm has a very simple structure, and is highly parallelizable. On general graphs of bounded degree, our reconstruction algorithm has subquadratic query complexity.
Cite as

Claire Mathieu and Hang Zhou. A Simple Algorithm for Graph Reconstruction. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 68:1-68:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{mathieu_et_al:LIPIcs.ESA.2021.68,
  author =	{Mathieu, Claire and Zhou, Hang},
  title =	{{A Simple Algorithm for Graph Reconstruction}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{68:1--68:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.68},
  URN =		{urn:nbn:de:0030-drops-146496},
  doi =		{10.4230/LIPIcs.ESA.2021.68},
  annote =	{Keywords: reconstruction, network topology, random regular graphs, metric dimension}
}
  • Refine by Author
  • 21 Mathieu, Claire
  • 7 Zhou, Hang
  • 3 Huang, Chien-Chung
  • 3 Marx, Dániel
  • 2 Coja-Oghlan, Amin
  • Show More...

  • Refine by Classification
  • 6 Theory of computation → Approximation algorithms analysis
  • 3 Theory of computation → Graph algorithms analysis
  • 3 Theory of computation → Routing and network design problems
  • 3 Theory of computation → Streaming, sublinear and near linear time algorithms
  • 2 Mathematics of computing → Approximation algorithms
  • Show More...

  • Refine by Keyword
  • 10 approximation algorithms
  • 5 planar graphs
  • 4 capacitated vehicle routing
  • 3 Approximation Algorithms
  • 3 approximation
  • Show More...

  • Refine by Type
  • 76 document
  • 1 volume

  • Refine by Publication Year
  • 52 2016
  • 6 2024
  • 4 2023
  • 3 2017
  • 3 2021
  • Show More...

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact