7 Search Results for "Stein, Max"

Document
DOI: 10.4230/LIPIcs.ESA.2024.97
Engineering Edge Orientation Algorithms

Authors: Henrik Reinstädtler, Christian Schulz, and Bora Uçar

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out-degree of a vertex in the resulting directed graph. This problem, which is solvable in polynomial time, arises in many applications. An ongoing challenge in edge orientation algorithms is their scalability, particularly in handling large-scale networks with millions or billions of edges efficiently. We propose a novel algorithmic framework based on finding and manipulating simple paths to face this challenge. Our framework is based on an existing algorithm and allows many algorithmic choices. By carefully exploring these choices and engineering the underlying algorithms, we obtain an implementation which is more efficient and scalable than the current state-of-the-art. Our experiments demonstrate significant performance improvements compared to state-of-the-art solvers. On average our algorithm is 6.59 times faster when compared to the state-of-the-art.
Cite as

Henrik Reinstädtler, Christian Schulz, and Bora Uçar. Engineering Edge Orientation Algorithms. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 97:1-97:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2024.97,
  author =	{Reinst\"{a}dtler, Henrik and Schulz, Christian and U\c{c}ar, Bora},
  title =	{{Engineering Edge Orientation Algorithms}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{97:1--97:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.97},
  URN =		{urn:nbn:de:0030-drops-211682},
  doi =		{10.4230/LIPIcs.ESA.2024.97},
  annote =	{Keywords: edge orientation, pseudoarboricity, graph algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.14
Scheduling on a Stochastic Number of Machines

Authors: Moritz Buchem, Franziska Eberle, Hugo Kooki Kasuya Rosado, Kevin Schewior, and Andreas Wiese

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We consider a new scheduling problem on parallel identical machines in which the number of machines is initially not known, but it follows a given probability distribution. Only after all jobs are assigned to a given number of bags, the actual number of machines is revealed. Subsequently, the jobs need to be assigned to the machines without splitting the bags. This is the stochastic version of a related problem introduced by Stein and Zhong [SODA 2018, TALG 2020] and it is, for example, motivated by bundling jobs that need to be scheduled by data centers. We present two PTASs for the stochastic setting, computing job-to-bag assignments that (i) minimize the expected maximum machine load and (ii) maximize the expected minimum machine load (like in the Santa Claus problem), respectively. The former result follows by careful enumeration combined with known PTASs. For the latter result, we introduce an intricate dynamic program that we apply to a suitably rounded instance.
Cite as

Moritz Buchem, Franziska Eberle, Hugo Kooki Kasuya Rosado, Kevin Schewior, and Andreas Wiese. Scheduling on a Stochastic Number of Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{buchem_et_al:LIPIcs.APPROX/RANDOM.2024.14,
  author =	{Buchem, Moritz and Eberle, Franziska and Kasuya Rosado, Hugo Kooki and Schewior, Kevin and Wiese, Andreas},
  title =	{{Scheduling on a Stochastic Number of Machines}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.14},
  URN =		{urn:nbn:de:0030-drops-210073},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.14},
  annote =	{Keywords: scheduling, approximation algorithms, stochastic machines, makespan, max-min fair allocation, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.22
Incremental (1-ε)-Approximate Dynamic Matching in O(poly(1/ε)) Update Time

Authors: Joakim Blikstad and Peter Kiss

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

Abstract
In the dynamic approximate maximum bipartite matching problem we are given bipartite graph G undergoing updates and our goal is to maintain a matching of G which is large compared the maximum matching size μ(G). We define a dynamic matching algorithm to be α (respectively (α, β))-approximate if it maintains matching M such that at all times |M | ≥ μ(G) ⋅ α (respectively |M| ≥ μ(G) ⋅ α - β). We present the first deterministic (1-ε)-approximate dynamic matching algorithm with O(poly(ε^{-1})) amortized update time for graphs undergoing edge insertions. Previous solutions either required super-constant [Gupta FSTTCS'14, Bhattacharya-Kiss-Saranurak SODA'23] or exponential in 1/ε [Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA'19] update time. Our implementation is arguably simpler than the mentioned algorithms and its description is self contained. Moreover, we show that if we allow for additive (1, ε⋅n)-approximation our algorithm seamlessly extends to also handle vertex deletions, on top of edge insertions. This makes our algorithm one of the few small update time algorithms for (1-ε)-approximate dynamic matching allowing for updates both increasing and decreasing the maximum matching size of G in a fully dynamic manner. Our algorithm relies on the weighted variant of the celebrated Edge-Degree-Constrained-Subgraph (EDCS) datastructure introduced by [Bernstein-Stein ICALP'15]. As far as we are aware we introduce the first application of the weighted-EDCS for arbitrarily dense graphs. We also present a significantly simplified proof for the approximation ratio of weighed-EDCS as a matching sparsifier compared to [Bernstein-Stein], as well as simple descriptions of a fractional matching and fractional vertex cover defined on top of the EDCS. Considering the wide range of applications EDCS has found in settings such as streaming, sub-linear, stochastic and more we hope our techniques will be of independent research interest outside of the dynamic setting.
Cite as

Joakim Blikstad and Peter Kiss. Incremental (1-ε)-Approximate Dynamic Matching in O(poly(1/ε)) Update Time. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{blikstad_et_al:LIPIcs.ESA.2023.22,
  author =	{Blikstad, Joakim and Kiss, Peter},
  title =	{{Incremental (1-\epsilon)-Approximate Dynamic Matching in O(poly(1/\epsilon)) Update Time}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{22:1--22:19},
  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.2023.22},
  URN =		{urn:nbn:de:0030-drops-186756},
  doi =		{10.4230/LIPIcs.ESA.2023.22},
  annote =	{Keywords: Bipartite Matching, Incremental Matching, Dynamic Algorithms, Approximation Algorithms, EDCS}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.24
Faster 0-1-Knapsack via Near-Convex Min-Plus-Convolution

Authors: Karl Bringmann and Alejandro Cassis

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

Abstract
We revisit the classic 0-1-Knapsack problem, in which we are given n items with their weights and profits as well as a weight budget W, and the goal is to find a subset of items of total weight at most W that maximizes the total profit. We study pseudopolynomial-time algorithms parameterized by the largest profit of any item p_{max}, and the largest weight of any item w_max. Our main result are algorithms for 0-1-Knapsack running in time Õ(n w_max p_max^{2/3}) and Õ(n p_max w_max^{2/3}), improving upon an algorithm in time O(n p_max w_max) by Pisinger [J. Algorithms '99]. In the regime p_max ≈ w_max ≈ n (and W ≈ OPT ≈ n²) our algorithms are the first to break the cubic barrier n³. To obtain our result, we give an efficient algorithm to compute the min-plus convolution of near-convex functions. More precisely, we say that a function f : [n] ↦ ℤ is Δ-near convex with Δ ≥ 1, if there is a convex function f ̆ such that f ̆(i) ≤ f(i) ≤ f ̆(i) + Δ for every i. We design an algorithm computing the min-plus convolution of two Δ-near convex functions in time Õ(nΔ). This tool can replace the usage of the prediction technique of Bateni, Hajiaghayi, Seddighin and Stein [STOC '18] in all applications we are aware of, and we believe it has wider applicability.
Cite as

Karl Bringmann and Alejandro Cassis. Faster 0-1-Knapsack via Near-Convex Min-Plus-Convolution. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bringmann_et_al:LIPIcs.ESA.2023.24,
  author =	{Bringmann, Karl and Cassis, Alejandro},
  title =	{{Faster 0-1-Knapsack via Near-Convex Min-Plus-Convolution}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{24:1--24:16},
  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.2023.24},
  URN =		{urn:nbn:de:0030-drops-186776},
  doi =		{10.4230/LIPIcs.ESA.2023.24},
  annote =	{Keywords: Knapsack, Fine-Grained Complexity, Min-Plus Convolution}
}
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)

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@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
DOI: 10.4230/LIPIcs.ESA.2021.60
Telescoping Filter: A Practical Adaptive Filter

Authors: David J. Lee, Samuel McCauley, Shikha Singh, and Max Stein

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

Abstract
Filters are small, fast, and approximate set membership data structures. They are often used to filter out expensive accesses to a remote set S for negative queries (that is, filtering out queries x ∉ S). Filters have one-sided errors: on a negative query, a filter may say "present" with a tunable false-positive probability of ε. Correctness is traded for space: filters only use log (1/ε) + O(1) bits per element. The false-positive guarantees of most filters, however, hold only for a single query. In particular, if x is a false positive, a subsequent query to x is a false positive with probability 1, not ε. With this in mind, recent work has introduced the notion of an adaptive filter. A filter is adaptive if each query is a false positive with probability ε, regardless of answers to previous queries. This requires "fixing" false positives as they occur. Adaptive filters not only provide strong false positive guarantees in adversarial environments but also improve query performance on practical workloads by eliminating repeated false positives. Existing work on adaptive filters falls into two categories. On the one hand, there are practical filters, based on the cuckoo filter, that attempt to fix false positives heuristically without meeting the adaptivity guarantee. On the other hand, the broom filter is a very complex adaptive filter that meets the optimal theoretical bounds. In this paper, we bridge this gap by designing the telescoping adaptive filter (TAF), a practical, provably adaptive filter. We provide theoretical false-positive and space guarantees for our filter, along with empirical results where we compare its performance against state-of-the-art filters. We also implement the broom filter and compare it to the TAF. Our experiments show that theoretical adaptivity can lead to improved false-positive performance on practical inputs, and can be achieved while maintaining throughput that is similar to non-adaptive filters.
Cite as

David J. Lee, Samuel McCauley, Shikha Singh, and Max Stein. Telescoping Filter: A Practical Adaptive Filter. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lee_et_al:LIPIcs.ESA.2021.60,
  author =	{Lee, David J. and McCauley, Samuel and Singh, Shikha and Stein, Max},
  title =	{{Telescoping Filter: A Practical Adaptive Filter}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{60:1--60:18},
  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.2021.60},
  URN =		{urn:nbn:de:0030-drops-146410},
  doi =		{10.4230/LIPIcs.ESA.2021.60},
  annote =	{Keywords: Filters, approximate-membership query data structures (AMQs), Bloom filters, quotient filters, cuckoo filters, adaptivity, succinct data structures}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.10
Routing in Polygonal Domains

Authors: Bahareh Banyassady, Man-Kwun Chiu, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, and Max Willert

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P , where each step must use only the label of the target node q and the routing table of the current node. For any fixed eps > 0, we pre ent a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + eps. The labels have O(log n) bits, and the routing tables are of size O((eps^{-1} + h) log n). The preprocessing time is O(n^2 log n + hn^2 + eps^{-1}hn). It can be improved to O(n 2 + eps^{-1}n) for simple polygons.
Cite as

Bahareh Banyassady, Man-Kwun Chiu, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, and Max Willert. Routing in Polygonal Domains. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{banyassady_et_al:LIPIcs.ISAAC.2017.10,
  author =	{Banyassady, Bahareh and Chiu, Man-Kwun and Korman, Matias and Mulzer, Wolfgang and van Renssen, Andr\'{e} and Roeloffzen, Marcel and Seiferth, Paul and Stein, Yannik and Vogtenhuber, Birgit and Willert, Max},
  title =	{{Routing in Polygonal Domains}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.10},
  URN =		{urn:nbn:de:0030-drops-82379},
  doi =		{10.4230/LIPIcs.ISAAC.2017.10},
  annote =	{Keywords: polygonal domains, routing scheme, small stretch,Yao graph}
}
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