7 Search Results for "Jabal Ameli, Afrouz"

Document
DOI: 10.4230/LIPIcs.SEA.2024.11
Engineering Weighted Connectivity Augmentation Algorithms

Authors: Marcelo Fonseca Faraj, Ernestine Großmann, Felix Joos, Thomas Möller, and Christian Schulz

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find a minimum cost subset of a given set of weighted links that increases the connectivity of a graph by one when the links are added to the edge set of the input instance. In this work, we give a first implementation of recently discovered better-than-2 approximations. Furthermore, we propose three new heuristics and one exact approach. These include a greedy algorithm considering link costs and the number of unique cuts covered, an approach based on minimum spanning trees and a local search algorithm that may improve a given solution by swapping links of paths. Our exact approach uses an ILP formulation with efficient cut enumeration as well as a fast initialization routine. We then perform an extensive experimental evaluation which shows that our algorithms are faster and yield the best solutions compared to the current state-of-the-art as well as the recently discovered better-than-2 approximation algorithms. Our novel local search algorithm can improve solution quality even further.
Cite as

Marcelo Fonseca Faraj, Ernestine Großmann, Felix Joos, Thomas Möller, and Christian Schulz. Engineering Weighted Connectivity Augmentation Algorithms. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{faraj_et_al:LIPIcs.SEA.2024.11,
  author =	{Faraj, Marcelo Fonseca and Gro{\ss}mann, Ernestine and Joos, Felix and M\"{o}ller, Thomas and Schulz, Christian},
  title =	{{Engineering Weighted Connectivity Augmentation Algorithms}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{11:1--11:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.11},
  URN =		{urn:nbn:de:0030-drops-203768},
  doi =		{10.4230/LIPIcs.SEA.2024.11},
  annote =	{Keywords: weighted connectivity augmentation, approximation, heuristic, integer linear program, algorithm engineering}
}
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)

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@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.2023.29
A 4/3 Approximation for 2-Vertex-Connectivity

Authors: Miguel Bosch-Calvo, Fabrizio Grandoni, and Afrouz Jabal Ameli

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

Abstract
The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph G. Our goal is to find a subgraph S of G with the minimum number of edges which is 2-vertex-connected, namely S remains connected after the deletion of an arbitrary node. 2VCSS is well-studied in terms of approximation algorithms, and the current best (polynomial-time) approximation factor is 10/7 by Heeger and Vygen [SIDMA'17] (improving on earlier results by Khuller and Vishkin [STOC'92] and Garg, Vempala and Singla [SODA'93]). Here we present an improved 4/3 approximation. Our main technical ingredient is an approximation preserving reduction to a conveniently structured subset of instances which are "almost" 3-vertex-connected. The latter reduction might be helpful in future work.
Cite as

Miguel Bosch-Calvo, Fabrizio Grandoni, and Afrouz Jabal Ameli. A 4/3 Approximation for 2-Vertex-Connectivity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{boschcalvo_et_al:LIPIcs.ICALP.2023.29,
  author =	{Bosch-Calvo, Miguel and Grandoni, Fabrizio and Jabal Ameli, Afrouz},
  title =	{{A 4/3 Approximation for 2-Vertex-Connectivity}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{29:1--29:13},
  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.2023.29},
  URN =		{urn:nbn:de:0030-drops-180813},
  doi =		{10.4230/LIPIcs.ICALP.2023.29},
  annote =	{Keywords: Algorithm, Network Design, Vertex-Connectivity, Approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.79
Finding Almost Tight Witness Trees

Authors: Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità

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

Abstract
This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in the analysis of the best approximation algorithms for two fundamental network design problems: Steiner Tree and Node-Tree Augmentation. We will show how a wiser choice of witness trees leads to an improved approximation for Node-Tree Augmentation, and for Steiner Tree in special classes of graphs.
Cite as

Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità. Finding Almost Tight Witness Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hyattdenesik_et_al:LIPIcs.ICALP.2023.79,
  author =	{Hyatt-Denesik, Dylan and Jabal Ameli, Afrouz and Sanit\`{a}, Laura},
  title =	{{Finding Almost Tight Witness Trees}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{79:1--79:16},
  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.2023.79},
  URN =		{urn:nbn:de:0030-drops-181314},
  doi =		{10.4230/LIPIcs.ICALP.2023.79},
  annote =	{Keywords: Algorithms, Network Design, Approximation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.71
Approximation Algorithms for Round-UFP and Round-SAP

Authors: Debajyoti Kar, Arindam Khan, and Andreas Wiese

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

Abstract
We study Round-UFP and Round-SAP, two generalizations of the classical Bin Packing problem that correspond to the unsplittable flow problem on a path (UFP) and the storage allocation problem (SAP), respectively. We are given a path with capacities on its edges and a set of jobs where for each job we are given a demand and a subpath. In Round-UFP, the goal is to find a packing of all jobs into a minimum number of copies (rounds) of the given path such that for each copy, the total demand of jobs on any edge does not exceed the capacity of the respective edge. In Round-SAP, the jobs are considered to be rectangles and the goal is to find a non-overlapping packing of these rectangles into a minimum number of rounds such that all rectangles lie completely below the capacity profile of the edges. We show that in contrast to Bin Packing, both problems do not admit an asymptotic polynomial-time approximation scheme (APTAS), even when all edge capacities are equal. However, for this setting, we obtain asymptotic (2+ε)-approximations for both problems. For the general case, we obtain an O(log log n)-approximation algorithm and an O(log log 1/δ)-approximation under (1+δ)-resource augmentation for both problems. For the intermediate setting of the no bottleneck assumption (i.e., the maximum job demand is at most the minimum edge capacity), we obtain an absolute 12- and an asymptotic (16+ε)-approximation algorithm for Round-UFP and Round-SAP, respectively.
Cite as

Debajyoti Kar, Arindam Khan, and Andreas Wiese. Approximation Algorithms for Round-UFP and Round-SAP. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kar_et_al:LIPIcs.ESA.2022.71,
  author =	{Kar, Debajyoti and Khan, Arindam and Wiese, Andreas},
  title =	{{Approximation Algorithms for Round-UFP and Round-SAP}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{71:1--71:19},
  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.2022.71},
  URN =		{urn:nbn:de:0030-drops-170098},
  doi =		{10.4230/LIPIcs.ESA.2022.71},
  annote =	{Keywords: Approximation Algorithms, Scheduling, Rectangle Packing}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.20
Approximation Algorithms for Demand Strip Packing

Authors: Waldo Gálvez, Fabrizio Grandoni, Afrouz Jabal Ameli, and Kamyar Khodamoradi

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
In the Demand Strip Packing problem (DSP), we are given a time interval and a collection of tasks, each characterized by a processing time and a demand for a given resource (such as electricity, computational power, etc.). A feasible solution consists of a schedule of the tasks within the mentioned time interval. Our goal is to minimize the peak resource consumption, i.e. the maximum total demand of tasks executed at any point in time. It is known that DSP is NP-hard to approximate below a factor 3/2, and standard techniques for related problems imply a (polynomial-time) 2-approximation. Our main result is a (5/3+ε)-approximation algorithm for any constant ε > 0. We also achieve best-possible approximation factors for some relevant special cases.
Cite as

Waldo Gálvez, Fabrizio Grandoni, Afrouz Jabal Ameli, and Kamyar Khodamoradi. Approximation Algorithms for Demand Strip Packing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 20:1-20:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{galvez_et_al:LIPIcs.APPROX/RANDOM.2021.20,
  author =	{G\'{a}lvez, Waldo and Grandoni, Fabrizio and Ameli, Afrouz Jabal and Khodamoradi, Kamyar},
  title =	{{Approximation Algorithms for Demand Strip Packing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{20:1--20:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.20},
  URN =		{urn:nbn:de:0030-drops-147130},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.20},
  annote =	{Keywords: Strip Packing, Two-Dimensional Packing, Approximation Algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.44
A Tight (3/2+ε) Approximation for Skewed Strip Packing

Authors: Waldo Gálvez, Fabrizio Grandoni, Afrouz Jabal Ameli, Klaus Jansen, Arindam Khan, and Malin Rau

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
In the Strip Packing problem, we are given a vertical half-strip [0,W]× [0,+∞) and a collection of open rectangles of width at most W. Our goal is to find an axis-aligned (non-overlapping) packing of such rectangles into the strip such that the maximum height OPT spanned by the packing is as small as possible. Strip Packing generalizes classical well-studied problems such as Makespan Minimization on identical machines (when rectangle widths are identical) and Bin Packing (when rectangle heights are identical). It has applications in manufacturing, scheduling and energy consumption in smart grids among others. It is NP-hard to approximate this problem within a factor (3/2-ε) for any constant ε > 0 by a simple reduction from the Partition problem. The current best approximation factor for Strip Packing is (5/3+ε) by Harren et al. [Computational Geometry '14], and it is achieved with a fairly complex algorithm and analysis. It seems plausible that Strip Packing admits a (3/2+ε)-approximation. We make progress in that direction by achieving such tight approximation guarantees for a special family of instances, which we call skewed instances. As standard in the area, for a given constant parameter δ > 0, we call large the rectangles with width at least δ W and height at least δ OPT, and skewed the remaining rectangles. If all the rectangles in the input are large, then one can easily compute the optimal packing in polynomial time (since the input can contain only a constant number of rectangles). We consider the complementary case where all the rectangles are skewed. This second case retains a large part of the complexity of the original problem; in particular, it is NP-hard to approximate within a factor (3/2-ε) and we provide an (almost) tight (3/2+ε)-approximation algorithm.
Cite as

Waldo Gálvez, Fabrizio Grandoni, Afrouz Jabal Ameli, Klaus Jansen, Arindam Khan, and Malin Rau. A Tight (3/2+ε) Approximation for Skewed Strip Packing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{galvez_et_al:LIPIcs.APPROX/RANDOM.2020.44,
  author =	{G\'{a}lvez, Waldo and Grandoni, Fabrizio and Ameli, Afrouz Jabal and Jansen, Klaus and Khan, Arindam and Rau, Malin},
  title =	{{A Tight (3/2+\epsilon) Approximation for Skewed Strip Packing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{44:1--44:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.44},
  URN =		{urn:nbn:de:0030-drops-126478},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.44},
  annote =	{Keywords: strip packing, approximation algorithm}
}
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