97 Search Results for "Sankowski, Piotr"

Volume

LIPIcs, Volume 57

24th Annual European Symposium on Algorithms (ESA 2016)

ESA 2016, August 22-24, 2016, Aarhus, Denmark

Editors: Piotr Sankowski and Christos Zaroliagis

Document
DOI: 10.4230/LIPIcs.ISAAC.2024.49
Online Multi-Level Aggregation with Delays and Stochastic Arrivals

Authors: Mathieu Mari, Michał Pawłowski, Runtian Ren, and Piotr Sankowski

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
This paper presents a new research direction for online Multi-Level Aggregation (MLA) with delays. Given an edge-weighted rooted tree T as input, a sequence of requests arriving at its vertices needs to be served in an online manner. A request r is characterized by two parameters: its arrival time t(r) > 0 and location l(r) being a vertex in tree T. Once r arrives, we can either serve it immediately or postpone this action until any time t > t(r). A request that has not been served at its arrival time is called pending up to the moment it gets served. We can serve several pending requests at the same time, paying a service cost equal to the weight of the subtree containing the locations of all the requests served and the root of T. Postponing the service of a request r to time t > t(r) generates an additional delay cost of t - t(r). The goal is to serve all requests in an online manner such that the total cost (i.e., the total sum of service and delay costs) is minimized. The MLA problem is a generalization of several well-studied problems, including the TCP Acknowledgment (trees of depth 1), Joint Replenishment (depth 2), and Multi-Level Message Aggregation (arbitrary depth). The current best algorithm achieves a competitive ratio of O(d²), where d denotes the depth of the tree. Here, we consider a stochastic version of MLA where the requests follow a Poisson arrival process. We present a deterministic online algorithm that achieves a constant ratio of expectations, meaning that the ratio between the expected costs of the solution generated by our algorithm and the optimal offline solution is bounded by a constant. Our algorithm is obtained by carefully combining two strategies. In the first one, we plan periodic oblivious visits to the subset of frequent vertices, whereas, in the second one, we greedily serve the pending requests in the remaining vertices. This problem is complex enough to demonstrate a very rare phenomenon that "single-minded" or "sample-average" strategies are not enough in stochastic optimization.
Cite as

Mathieu Mari, Michał Pawłowski, Runtian Ren, and Piotr Sankowski. Online Multi-Level Aggregation with Delays and Stochastic Arrivals. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 49:1-49:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mari_et_al:LIPIcs.ISAAC.2024.49,
  author =	{Mari, Mathieu and Paw{\l}owski, Micha{\l} and Ren, Runtian and Sankowski, Piotr},
  title =	{{Online Multi-Level Aggregation with Delays and Stochastic Arrivals}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{49:1--49:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.49},
  URN =		{urn:nbn:de:0030-drops-221768},
  doi =		{10.4230/LIPIcs.ISAAC.2024.49},
  annote =	{Keywords: online algorithms, online network design, stochastic model, Poisson arrivals}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.90
Dynamic PageRank: Algorithms and Lower Bounds

Authors: Rajesh Jayaram, Jakub Łącki, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski

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

Abstract
We consider the PageRank problem in the dynamic setting, where the goal is to explicitly maintain an approximate PageRank vector π ∈ ℝⁿ for a graph under a sequence of edge insertions and deletions. Our main result is a complete characterization of the complexity of dynamic PageRank maintenance for both multiplicative and additive (L₁) approximations. First, we establish matching lower and upper bounds for maintaining additive approximate PageRank in both incremental and decremental settings. In particular, we demonstrate that in the worst-case (1/α)^{Θ(log log n)} update time is necessary and sufficient for this problem, where α is the desired additive approximation. On the other hand, we demonstrate that the commonly employed ForwardPush approach performs substantially worse than this optimal runtime. Specifically, we show that ForwardPush requires Ω(n^{1-δ}) time per update on average, for any δ > 0, even in the incremental setting. For multiplicative approximations, however, we demonstrate that the situation is significantly more challenging. Specifically, we prove that any algorithm that explicitly maintains a constant factor multiplicative approximation of the PageRank vector of a directed graph must have amortized update time Ω(n^{1-δ}), for any δ > 0, even in the incremental setting, thereby resolving a 13-year old open question of Bahmani et al. (VLDB 2010). This sharply contrasts with the undirected setting, where we show that poly log n update time is feasible, even in the fully dynamic setting under oblivious adversary.
Cite as

Rajesh Jayaram, Jakub Łącki, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski. Dynamic PageRank: Algorithms and Lower Bounds. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 90:1-90:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jayaram_et_al:LIPIcs.ICALP.2024.90,
  author =	{Jayaram, Rajesh and {\L}\k{a}cki, Jakub and Mitrovi\'{c}, Slobodan and Onak, Krzysztof and Sankowski, Piotr},
  title =	{{Dynamic PageRank: Algorithms and Lower Bounds}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{90:1--90:19},
  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.2024.90},
  URN =		{urn:nbn:de:0030-drops-202336},
  doi =		{10.4230/LIPIcs.ICALP.2024.90},
  annote =	{Keywords: PageRank, dynamic algorithms, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.57
A Strongly Polynomial-Time Algorithm for Weighted General Factors with Three Feasible Degrees

Authors: Shuai Shao and Stanislav Živný

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
General factors are a generalization of matchings. Given a graph G with a set π(v) of feasible degrees, called a degree constraint, for each vertex v of G, the general factor problem is to find a (spanning) subgraph F of G such that deg_F(v) ∈ π(v) for every v of G. When all degree constraints are symmetric Δ-matroids, the problem is solvable in polynomial time. The weighted general factor problem is to find a general factor of the maximum total weight in an edge-weighted graph. Strongly polynomial-time algorithms are only known for weighted general factor problems that are reducible to the weighted matching problem by gadget constructions. In this paper, we present a strongly polynomial-time algorithm for a type of weighted general factor problems with real-valued edge weights that is provably not reducible to the weighted matching problem by gadget constructions. As an application, we obtain a strongly polynomial-time algorithm for the terminal backup problem by reducing it to the weighted general factor problem.
Cite as

Shuai Shao and Stanislav Živný. A Strongly Polynomial-Time Algorithm for Weighted General Factors with Three Feasible Degrees. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 57:1-57:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shao_et_al:LIPIcs.ISAAC.2023.57,
  author =	{Shao, Shuai and \v{Z}ivn\'{y}, Stanislav},
  title =	{{A Strongly Polynomial-Time Algorithm for Weighted General Factors with Three Feasible Degrees}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{57:1--57:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.57},
  URN =		{urn:nbn:de:0030-drops-193597},
  doi =		{10.4230/LIPIcs.ISAAC.2023.57},
  annote =	{Keywords: matchings, factors, edge constraint satisfaction problems, terminal backup problem, delta matroids}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.84
Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs

Authors: Adam Karczmarz and Piotr Sankowski

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

Abstract
We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with Õ(mn^{4/5}) worst-case update time processing arbitrary s,t-distance queries in Õ(n^{4/5}) time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs. Moreover, we give a Monte Carlo randomized fully dynamic reachability data structure processing single-edge updates in Õ(n√m) worst-case time and queries in O(√m) time. For sparse digraphs, such a tradeoff has only been previously described with amortized update time [Roditty and Zwick, SIAM J. Comp. 2008].
Cite as

Adam Karczmarz and Piotr Sankowski. Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 84:1-84:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{karczmarz_et_al:LIPIcs.ICALP.2023.84,
  author =	{Karczmarz, Adam and Sankowski, Piotr},
  title =	{{Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{84:1--84:20},
  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.2023.84},
  URN =		{urn:nbn:de:0030-drops-181363},
  doi =		{10.4230/LIPIcs.ICALP.2023.84},
  annote =	{Keywords: dynamic shortest paths, dynamic reachability, dynamic transitive closure}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.46
Sublinear Average-Case Shortest Paths in Weighted Unit-Disk Graphs

Authors: Adam Karczmarz, Jakub Pawlewicz, and Piotr Sankowski

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
We consider the problem of computing shortest paths in weighted unit-disk graphs in constant dimension d. Although the single-source and all-pairs variants of this problem are well-studied in the plane case, no non-trivial exact distance oracles for unit-disk graphs have been known to date, even for d = 2. The classical result of Sedgewick and Vitter [Algorithmica '86] shows that for weighted unit-disk graphs in the plane the A^* search has average-case performance superior to that of a standard shortest path algorithm, e.g., Dijkstra’s algorithm. Specifically, if the n corresponding points of a weighted unit-disk graph G are picked from a unit square uniformly at random, and the connectivity radius is r ∈ (0,1), A^* finds a shortest path in G in O(n) expected time when r = Ω(√{log n/n}), even though G has Θ((nr)²) edges in expectation. In other words, the work done by the algorithm is in expectation proportional to the number of vertices and not the number of edges. In this paper, we break this natural barrier and show even stronger sublinear time results. We propose a new heuristic approach to computing point-to-point exact shortest paths in unit-disk graphs. We analyze the average-case behavior of our heuristic using the same random graph model as used by Sedgewick and Vitter and prove it superior to A^*. Specifically, we show that, if we are able to report the set of all k points of G from an arbitrary rectangular region of the plane in O(k + t(n)) time, then a shortest path between arbitrary two points of such a random graph on the plane can be found in O(1/r² + t(n)) expected time. In particular, the state-of-the-art range reporting data structures imply a sublinear expected bound for all r = Ω(√{log n/n}) and O(√n) expected bound for r = Ω(n^{-1/4}) after only near-linear preprocessing of the point set. Our approach naturally generalizes to higher dimensions d ≥ 3 and yields sublinear expected bounds for all d = O(1) and sufficiently large r.
Cite as

Adam Karczmarz, Jakub Pawlewicz, and Piotr Sankowski. Sublinear Average-Case Shortest Paths in Weighted Unit-Disk Graphs. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{karczmarz_et_al:LIPIcs.SoCG.2021.46,
  author =	{Karczmarz, Adam and Pawlewicz, Jakub and Sankowski, Piotr},
  title =	{{Sublinear Average-Case Shortest Paths in Weighted Unit-Disk Graphs}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.46},
  URN =		{urn:nbn:de:0030-drops-138454},
  doi =		{10.4230/LIPIcs.SoCG.2021.46},
  annote =	{Keywords: unit-disk graphs, shortest paths, distance oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.66
Min-Cost Flow in Unit-Capacity Planar Graphs

Authors: Adam Karczmarz and Piotr Sankowski

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
In this paper we give an O~((nm)^(2/3) log C) time algorithm for computing min-cost flow (or min-cost circulation) in unit capacity planar multigraphs where edge costs are integers bounded by C. For planar multigraphs, this improves upon the best known algorithms for general graphs: the O~(m^(10/7) log C) time algorithm of Cohen et al. [SODA 2017], the O(m^(3/2) log(nC)) time algorithm of Gabow and Tarjan [SIAM J. Comput. 1989] and the O~(sqrt(n) m log C) time algorithm of Lee and Sidford [FOCS 2014]. In particular, our result constitutes the first known fully combinatorial algorithm that breaks the Omega(m^(3/2)) time barrier for min-cost flow problem in planar graphs. To obtain our result we first give a very simple successive shortest paths based scaling algorithm for unit-capacity min-cost flow problem that does not explicitly operate on dual variables. This algorithm also runs in O~(m^(3/2) log C) time for general graphs, and, to the best of our knowledge, it has not been described before. We subsequently show how to implement this algorithm faster on planar graphs using well-established tools: r-divisions and efficient algorithms for computing (shortest) paths in so-called dense distance graphs.
Cite as

Adam Karczmarz and Piotr Sankowski. Min-Cost Flow in Unit-Capacity Planar Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 66:1-66:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{karczmarz_et_al:LIPIcs.ESA.2019.66,
  author =	{Karczmarz, Adam and Sankowski, Piotr},
  title =	{{Min-Cost Flow in Unit-Capacity Planar Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{66:1--66:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.66},
  URN =		{urn:nbn:de:0030-drops-111878},
  doi =		{10.4230/LIPIcs.ESA.2019.66},
  annote =	{Keywords: minimum-cost flow, minimum-cost circulation, planar graphs}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.21
Planar Maximum Matching: Towards a Parallel Algorithm

Authors: Samir Datta, Raghav Kulkarni, Ashish Kumar, and Anish Mukherjee

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Perfect matchings in planar graphs have been extensively studied and understood in the context of parallel complexity [P W Kastelyn, 1967; Vijay Vazirani, 1988; Meena Mahajan and Kasturi R. Varadarajan, 2000; Datta et al., 2010; Nima Anari and Vijay V. Vazirani, 2017]. However, corresponding results for maximum matchings have been elusive. We partly bridge this gap by proving: 1) An SPL upper bound for planar bipartite maximum matching search. 2) Planar maximum matching search reduces to planar maximum matching decision. 3) Planar maximum matching count reduces to planar bipartite maximum matching count and planar maximum matching decision. The first bound improves on the known [Thanh Minh Hoang, 2010] bound of L^{C_=L} and is adaptable to any special bipartite graph class with non-zero circulation such as bounded genus graphs, K_{3,3}-free graphs and K_5-free graphs. Our bounds and reductions non-trivially combine techniques like the Gallai-Edmonds decomposition [L. Lovász and M.D. Plummer, 1986], deterministic isolation [Datta et al., 2010; Samir Datta et al., 2012; Rahul Arora et al., 2016], and the recent breakthroughs in the parallel search for planar perfect matchings [Nima Anari and Vijay V. Vazirani, 2017; Piotr Sankowski, 2018].
Cite as

Samir Datta, Raghav Kulkarni, Ashish Kumar, and Anish Mukherjee. Planar Maximum Matching: Towards a Parallel Algorithm. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{datta_et_al:LIPIcs.ISAAC.2018.21,
  author =	{Datta, Samir and Kulkarni, Raghav and Kumar, Ashish and Mukherjee, Anish},
  title =	{{Planar Maximum Matching: Towards a Parallel Algorithm}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.21},
  URN =		{urn:nbn:de:0030-drops-99695},
  doi =		{10.4230/LIPIcs.ISAAC.2018.21},
  annote =	{Keywords: maximum matching, planar graphs, parallel complexity, reductions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.21
Online Facility Location with Deletions

Authors: Marek Cygan, Artur Czumaj, Marcin Mucha, and Piotr Sankowski

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
In this paper we study three previously unstudied variants of the online Facility Location problem, considering an intrinsic scenario when the clients and facilities are not only allowed to arrive to the system, but they can also depart at any moment. We begin with the study of a natural fully-dynamic online uncapacitated model where clients can be both added and removed. When a client arrives, then it has to be assigned either to an existing facility or to a new facility opened at the client's location. However, when a client who has been also one of the open facilities is to be removed, then our model has to allow to reconnect all clients that have been connected to that removed facility. In this model, we present an optimal O(log(n_{act}) / log log(n_{act}))-competitive algorithm, where n_{act} is the number of active clients at the end of the input sequence. Next, we turn our attention to the capacitated Facility Location problem. We first note that if no deletions are allowed, then one can achieve an optimal competitive ratio of O(log(n) / log(log n)), where n is the length of the sequence. However, when deletions are allowed, the capacitated version of the problem is significantly more challenging than the uncapacitated one. We show that still, using a more sophisticated algorithmic approach, one can obtain an online O(log N + log c log n)-competitive algorithm for the capacitated Facility Location problem in the fully dynamic model, where N is number of points in the input metric and c is the capacity of any open facility.
Cite as

Marek Cygan, Artur Czumaj, Marcin Mucha, and Piotr Sankowski. Online Facility Location with Deletions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cygan_et_al:LIPIcs.ESA.2018.21,
  author =	{Cygan, Marek and Czumaj, Artur and Mucha, Marcin and Sankowski, Piotr},
  title =	{{Online Facility Location with Deletions}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah 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.2018.21},
  URN =		{urn:nbn:de:0030-drops-94843},
  doi =		{10.4230/LIPIcs.ESA.2018.21},
  annote =	{Keywords: online algorithms, facility location, fully-dynamic online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.97
NC Algorithms for Weighted Planar Perfect Matching and Related Problems

Authors: Piotr Sankowski

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
Consider a planar graph G=(V,E) with polynomially bounded edge weight function w:E -> [0, poly(n)]. The main results of this paper are NC algorithms for finding minimum weight perfect matching in G. In order to solve this problems we develop a new relatively simple but versatile framework that is combinatorial in spirit. It handles the combinatorial structure of matchings directly and needs to only know weights of appropriately defined matchings from algebraic subroutines. Moreover, using novel planarity preserving reductions, we show how to find: maximum weight matching in G when G is bipartite; maximum multiple-source multiple-sink flow in G where c:E -> [1, poly(n)] is a polynomially bounded edge capacity function; minimum weight f-factor in G where f:V -> [1, poly(n)]; min-cost flow in G where c:E -> [1, poly(n)] is a polynomially bounded edge capacity function and b:V -> [1, poly(n)] is a polynomially bounded vertex demand function. There have been no known NC algorithms for these problems previously.
Cite as

Piotr Sankowski. NC Algorithms for Weighted Planar Perfect Matching and Related Problems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 97:1-97:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{sankowski:LIPIcs.ICALP.2018.97,
  author =	{Sankowski, Piotr},
  title =	{{NC Algorithms for Weighted Planar Perfect Matching and Related Problems}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{97:1--97:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.97},
  URN =		{urn:nbn:de:0030-drops-91011},
  doi =		{10.4230/LIPIcs.ICALP.2018.97},
  annote =	{Keywords: planar graph, NC algorithms, maximum cardinality matching, maximum weight matching, min-cost flow, maximum multiple-source multiple-sink flow, f-factors}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.63
Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}

Authors: Piotr Sankowski and Piotr Wygocki

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

Abstract
In this paper, we report progress on answering the open problem presented by Pagh [11], who considered the near neighbor search without false negatives for the Hamming distance. We show new data structures for solving the c-approximate near neighbors problem without false negatives for Euclidean high dimensional space \mathcal{R}^d. These data structures work for any c = \omega(\sqrt{\log{\log{n}}}), where n is the number of points in the input set, with poly-logarithmic query time and polynomial pre-processing time. This improves over the known algorithms, which require c to be \Omega(\sqrt{d}). This improvement is obtained by applying a sequence of reductions, which are interesting on their own. First, we reduce the problem to d instances of dimension logarithmic in n. Next, these instances are reduced to a number of c-approximate near neighbor search without false negatives instances in \big(\Rspace^k\big)^L space equipped with metric m(x,y) = \max_{1 \le i \leL}(\dist{x_i - y_i}_2).
Cite as

Piotr Sankowski and Piotr Wygocki. Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 63:1-63:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{sankowski_et_al:LIPIcs.ISAAC.2017.63,
  author =	{Sankowski, Piotr and Wygocki, Piotr},
  title =	{{Approximate Nearest Neighbors Search Without False Negatives For l\underline2 For c\ranglesqrt\{loglog\{n\}\}}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{63:1--63:12},
  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.2017.63},
  URN =		{urn:nbn:de:0030-drops-82189},
  doi =		{10.4230/LIPIcs.ISAAC.2017.63},
  annote =	{Keywords: locality sensitive hashing, approximate near neighbor search, high- dimensional, similarity search}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.50
Contracting a Planar Graph Efficiently

Authors: Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, Eva Rotenberg, and Piotr Sankowski

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges. By applying the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar graph problems, including decremental 2-vertex and 3-edge connectivity, and we show that using our data structure in a black-box manner, one obtains conceptually simple optimal algorithms for computing MST and 5-coloring in planar graphs.
Cite as

Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, Eva Rotenberg, and Piotr Sankowski. Contracting a Planar Graph Efficiently. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{holm_et_al:LIPIcs.ESA.2017.50,
  author =	{Holm, Jacob and Italiano, Giuseppe F. and Karczmarz, Adam and Lacki, Jakub and Rotenberg, Eva and Sankowski, Piotr},
  title =	{{Contracting a Planar Graph Efficiently}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.50},
  URN =		{urn:nbn:de:0030-drops-78755},
  doi =		{10.4230/LIPIcs.ESA.2017.50},
  annote =	{Keywords: planar graphs, algorithms, data structures, connectivity, coloring}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.20
Conditional Lower Bounds for All-Pairs Max-Flow

Authors: Robert Krauthgamer and Ohad Trabelsi

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We provide evidence that computing the maximum flow value between every pair of nodes in a directed graph on n nodes, m edges, and capacities in the range [1..n], which we call the All-Pairs Max-Flow problem, cannot be solved in time that is faster significantly (i.e., by a polynomial factor) than O(n^2 m). Since a single maximum st-flow in such graphs can be solved in time \tilde{O}(m\sqrt{n}) [Lee and Sidford, FOCS 2014], we conclude that the all-pairs version might require time equivalent to \tilde\Omega(n^{3/2}) computations of maximum st-flow, which strongly separates the directed case from the undirected one. Moreover, if maximum $st$-flow can be solved in time \tilde{O}(m), then the runtime of \tilde\Omega(n^2) computations is needed. This is in contrast to a conjecture of Lacki, Nussbaum, Sankowski, and Wulf-Nilsen [FOCS 2012] that All-Pairs Max-Flow in general graphs can be solved faster than the time of O(n^2) computations of maximum st-flow. Specifically, we show that in sparse graphs G=(V,E,w), if one can compute the maximum st-flow from every s in an input set of sources S\subseteq V to every t in an input set of sinks T\subseteq V in time O((|S||T|m)^{1-epsilon}), for some |S|, |T|, and a constant epsilon>0, then MAX-CNF-SAT (maximum satisfiability of conjunctive normal form formulas) with n' variables and m' clauses can be solved in time {m'}^{O(1)}2^{(1-delta)n'} for a constant delta(epsilon)>0, a problem for which not even 2^{n'}/\poly(n') algorithms are known. Such runtime for MAX-CNF-SAT would in particular refute the Strong Exponential Time Hypothesis (SETH). Hence, we improve the lower bound of Abboud, Vassilevska-Williams, and Yu [STOC 2015], who showed that for every fixed epsilon>0 and |S|=|T|=O(\sqrt{n}), if the above problem can be solved in time O(n^{3/2-epsilon}), then some incomparable (and intuitively weaker) conjecture is false. Furthermore, a larger lower bound than ours implies strictly super-linear time for maximum st-flow problem, which would be an amazing breakthrough. In addition, we show that All-Pairs Max-Flow in uncapacitated networks with every edge-density m=m(n), cannot be computed in time significantly faster than O(mn), even for acyclic networks. The gap to the fastest known algorithm by Cheung, Lau, and Leung [FOCS 2011] is a factor of O(m^{omega-1}/n), and for acyclic networks it is O(n^{omega-1}), where omega is the matrix multiplication exponent.
Cite as

Robert Krauthgamer and Ohad Trabelsi. Conditional Lower Bounds for All-Pairs Max-Flow. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{krauthgamer_et_al:LIPIcs.ICALP.2017.20,
  author =	{Krauthgamer, Robert and Trabelsi, Ohad},
  title =	{{Conditional Lower Bounds for All-Pairs Max-Flow}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.20},
  URN =		{urn:nbn:de:0030-drops-74264},
  doi =		{10.4230/LIPIcs.ICALP.2017.20},
  annote =	{Keywords: Conditional lower bounds, Hardness in P, All-Pairs Maximum Flow, Strong Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.56
Improved Distance Queries and Cycle Counting by Frobenius Normal Form

Authors: Piotr Sankowski and Karol Wegrzycki

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
Consider an unweighted, directed graph G with the diameter D. In this paper, we introduce the framework for counting cycles and walks of given length in matrix multiplication time O-tilde(n^omega). The framework is based on the fast decomposition into Frobenius normal form and the Hankel matrix-vector multiplication. It allows us to solve the following problems efficiently. * All Nodes Shortest Cycles - for every node return the length of the shortest cycle containing it. We give an O-tilde(n^omega) algorithm that improves the previous O-tilde(n^((omega + 3)/2)) algorithm for unweighted digraphs. * We show how to compute all D sets of vertices lying on cycles of length c in {1, ..., D} in randomized time O-tilde(n^omega). It improves upon an algorithm by Cygan where algorithm that computes a single set is presented. * We present a functional improvement of distance queries for directed, unweighted graphs. * All Pairs All Walks - we show almost optimal O-tilde(n^3) time algorithm for all walks counting problem. We improve upon the naive O(D n^omega) time algorithm.
Cite as

Piotr Sankowski and Karol Wegrzycki. Improved Distance Queries and Cycle Counting by Frobenius Normal Form. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{sankowski_et_al:LIPIcs.STACS.2017.56,
  author =	{Sankowski, Piotr and Wegrzycki, Karol},
  title =	{{Improved Distance Queries and Cycle Counting by Frobenius Normal Form}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{56:1--56:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.56},
  URN =		{urn:nbn:de:0030-drops-69773},
  doi =		{10.4230/LIPIcs.STACS.2017.56},
  annote =	{Keywords: Frobenius Normal Form, Graph Algorithms, All Nodes Shortest Cycles}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ESA.2016
LIPIcs, Volume 57, ESA'16, Complete Volume

Authors: Piotr Sankowski and Christos Zaroliagis

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
LIPIcs, Volume 57, ESA'16, Complete Volume
Cite as

24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Proceedings{sankowski_et_al:LIPIcs.ESA.2016,
  title =	{{LIPIcs, Volume 57, ESA'16, Complete Volume}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016},
  URN =		{urn:nbn:de:0030-drops-65854},
  doi =		{10.4230/LIPIcs.ESA.2016},
  annote =	{Keywords: Data Structures, Nonnumerical Algorithms and Problems, Optimization, Discrete Mathematics, Mathematical Software, Algorithms, Problem Solving, Control Methods and Search, Computational Geometry and Object Modeling}
}
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