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Volume

LIPIcs, Volume 244

30th Annual European Symposium on Algorithms (ESA 2022)

ESA 2022, September 5-9, 2022, Berlin/Potsdam, Germany

Editors: Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman

Document

DOI: 10.4230/LIPIcs.SEA.2024.14

Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions

Authors: Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu

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

Abstract

Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA transcript assembly and applications outside of Bioinformatics. We improve an existing ILP (Integer Linear Programming) model by Dias et al. [RECOMB 2022] for DAGs by decreasing the solver’s search space using solution safety and several other optimizations. This results in a significant speedup compared to the original ILP, of up to 34× on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in speedups that go up to 219× on the hardest instances. We also developed an ILP model of reduced dimensionality for an MFD variant in which the solution path weights are restricted to a given set. This model can find an optimal MFD solution for most instances, and overall, its accuracy significantly outperforms that of previous greedy algorithms while being up to an order of magnitude faster than our optimized ILP.

Cite as

Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu. Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grigorjew_et_al:LIPIcs.SEA.2024.14,
  author =	{Grigorjew, Andreas and Dias, Fernando H. C. and Cracco, Andrea and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{14:1--14:19},
  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.2024.14},
  URN =		{urn:nbn:de:0030-drops-203792},
  doi =		{10.4230/LIPIcs.SEA.2024.14},
  annote =	{Keywords: Flow decomposition, Integer Linear Programming, Safety, RNA-seq, RNA transcript assembly, isoform}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.54

Nearly Optimal Independence Oracle Algorithms for Edge Estimation in Hypergraphs

Authors: Holger Dell, John Lapinskas, and Kitty Meeks

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

Abstract

Consider a query model of computation in which an n-vertex k-hypergraph can be accessed only via its independence oracle or via its colourful independence oracle, and each oracle query may incur a cost depending on the size of the query. Several recent results (Dell and Lapinskas, STOC 2018; Dell, Lapinskas, and Meeks, SODA 2020) give efficient algorithms to approximately count the hypergraph’s edges in the colourful setting. These algorithms immediately imply fine-grained reductions from approximate counting to decision, with overhead only log^Θ(k) n over the running time n^α of the original decision algorithm, for many well-studied problems including k-Orthogonal Vectors, k-SUM, subgraph isomorphism problems including k-Clique and colourful-H, graph motifs, and k-variable first-order model checking. We explore the limits of what is achievable in this setting, obtaining unconditional lower bounds on the oracle cost of algorithms to approximately count the hypergraph’s edges in both the colourful and uncoloured settings. In both settings, we also obtain algorithms which essentially match these lower bounds; in the colourful setting, this requires significant changes to the algorithm of Dell, Lapinskas, and Meeks (SODA 2020) and reduces the total overhead to log^{Θ(k-α)}n. Our lower bound for the uncoloured setting shows that there is no fine-grained reduction from approximate counting to the corresponding uncoloured decision problem (except in the case α ≥ k-1): without an algorithm for the colourful decision problem, we cannot hope to avoid the much larger overhead of roughly n^{(k-α)²/4}. The uncoloured setting has previously been studied for the special case k = 2 (Peled, Ramamoorthy, Rashtchian, Sinha, ITCS 2018; Chen, Levi, and Waingarten, SODA 2020), and our work generalises the existing algorithms and lower bounds for this special case to k > 2 and to oracles with cost.

Cite as

Holger Dell, John Lapinskas, and Kitty Meeks. Nearly Optimal Independence Oracle Algorithms for Edge Estimation in Hypergraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dell_et_al:LIPIcs.ICALP.2024.54,
  author =	{Dell, Holger and Lapinskas, John and Meeks, Kitty},
  title =	{{Nearly Optimal Independence Oracle Algorithms for Edge Estimation in Hypergraphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{54:1--54:17},
  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.2024.54},
  URN =		{urn:nbn:de:0030-drops-201977},
  doi =		{10.4230/LIPIcs.ICALP.2024.54},
  annote =	{Keywords: Graph oracles, Fine-grained complexity, Approximate counting, Hypergraphs}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.71

Low-Memory Algorithms for Online Edge Coloring

Authors: Prantar Ghosh and Manuel Stoeckl

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

Abstract

For edge coloring, the online and the W-streaming models seem somewhat orthogonal: the former needs edges to be assigned colors immediately after insertion, typically without any space restrictions, while the latter limits memory to be sublinear in the input size but allows an edge’s color to be announced any time after its insertion. We aim for the best of both worlds by designing small-space online algorithms for edge coloring. Our online algorithms significantly improve upon the memory used by prior ones while achieving an O(1)-competitive ratio. We study the problem under both (adversarial) edge arrivals and vertex arrivals. Under vertex arrivals of any n-node graph with maximum vertex-degree Δ, our online O(Δ)-coloring algorithm uses only semi-streaming space (i.e., Õ(n) space, where the Õ(.) notation hides polylog(n) factors). Under edge arrivals, we obtain an online O(Δ)-coloring in Õ(n√Δ) space. We also achieve a smooth color-space tradeoff: for any t = O(Δ), we get an O(Δt(log²Δ))-coloring in Õ(n√{Δ/t}) space, improving upon the state of the art that used Õ(nΔ/t) space for the same number of colors. The improvements stem from extensive use of random permutations that enable us to avoid previously used colors. Most of our algorithms can be derandomized and extended to multigraphs, where edge coloring is known to be considerably harder than for simple graphs.

Cite as

Prantar Ghosh and Manuel Stoeckl. Low-Memory Algorithms for Online Edge Coloring. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ghosh_et_al:LIPIcs.ICALP.2024.71,
  author =	{Ghosh, Prantar and Stoeckl, Manuel},
  title =	{{Low-Memory Algorithms for Online Edge Coloring}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{71:1--71:19},
  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.2024.71},
  URN =		{urn:nbn:de:0030-drops-202146},
  doi =		{10.4230/LIPIcs.ICALP.2024.71},
  annote =	{Keywords: Edge coloring, streaming model, online algorithms}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.120

Caching Connections in Matchings

Authors: Yaniv Sadeh and Haim Kaplan

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

Abstract

Motivated by the desire to utilize a limited number of configurable optical switches by recent advances in Software Defined Networks (SDNs), we define an online problem which we call the Caching in Matchings problem. This problem has a natural combinatorial structure and therefore may find additional applications in theory and practice. In the Caching in Matchings problem our cache consists of k matchings of connections between servers that form a bipartite graph. To cache a connection we insert it into one of the k matchings possibly evicting at most two other connections from this matching. This problem resembles the problem known as Connection Caching [Cohen et al., 2000], where we also cache connections but our only restriction is that they form a graph with bounded degree k. Our results show a somewhat surprising qualitative separation between the problems: The competitive ratio of any online algorithm for caching in matchings must depend on the size of the graph. Specifically, we give a deterministic O(nk) competitive and randomized O(n log k) competitive algorithms for caching in matchings, where n is the number of servers and k is the number of matchings. We also show that the competitive ratio of any deterministic algorithm is Ω(max(n/k,k)) and of any randomized algorithm is Ω(log (n/(k² log k)) ⋅ log k). In particular, the lower bound for randomized algorithms is Ω(log n) regardless of k, and can be as high as Ω(log² n) if k = n^{1/3}, for example. We also show that if we allow the algorithm to use at least 2k-1 matchings compared to k used by the optimum then we match the competitive ratios of connection catching which are independent of n. Interestingly, we also show that even a single extra matching for the algorithm allows to get substantially better bounds.

Cite as

Yaniv Sadeh and Haim Kaplan. Caching Connections in Matchings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sadeh_et_al:LIPIcs.ICALP.2024.120,
  author =	{Sadeh, Yaniv and Kaplan, Haim},
  title =	{{Caching Connections in Matchings}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{120:1--120:20},
  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.2024.120},
  URN =		{urn:nbn:de:0030-drops-202639},
  doi =		{10.4230/LIPIcs.ICALP.2024.120},
  annote =	{Keywords: Caching, Matchings, Caching in Matchings, Edge Coloring, Online Algorithms}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2024.20

Sparsity-Parameterised Dynamic Edge Colouring

Authors: Aleksander B. G. Christiansen, Eva Rotenberg, and Juliette Vlieghe

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract

We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph’s arboricity, α. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm that updates a proper Δ + O(α) edge colouring in poly(log n) amortized time. Our algorithm is fully adaptive to the current value of the maximum degree and arboricity. In this fully-dynamic setting, the state-of-the-art edge-colouring algorithms are either a randomised algorithm using (1 + ε)Δ colours in poly(log n, ε^{-1}) time per update, or the naive greedy algorithm which is a deterministic 2Δ -1 edge colouring with log(Δ) update time. Compared to the (1+ε)Δ algorithm, our algorithm is deterministic and asymptotically faster, and when α is sufficiently small compared to Δ, it even uses fewer colours. In particular, ours is the first Δ+O(1) edge-colouring algorithm for dynamic forests, and dynamic planar graphs, with polylogarithmic update time. Additionally, in the static setting, we show that we can find a proper edge colouring with Δ + 2α colours in O(mlog n) time. Moreover, the colouring returned by our algorithm has the following local property: every edge uv is coloured with a colour in {1, max{deg(u), deg(v)} + 2α}. The time bound matches that of the greedy algorithm that computes a 2Δ-1 colouring of the graph’s edges, and improves the number of colours when α is sufficiently small compared to Δ.

Cite as

Aleksander B. G. Christiansen, Eva Rotenberg, and Juliette Vlieghe. Sparsity-Parameterised Dynamic Edge Colouring. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{christiansen_et_al:LIPIcs.SWAT.2024.20,
  author =	{Christiansen, Aleksander B. G. and Rotenberg, Eva and Vlieghe, Juliette},
  title =	{{Sparsity-Parameterised Dynamic Edge Colouring}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.20},
  URN =		{urn:nbn:de:0030-drops-200608},
  doi =		{10.4230/LIPIcs.SWAT.2024.20},
  annote =	{Keywords: edge colouring, arboricity, hierarchical partition, dynamic algorithms, amortized analysis}
}

Document

DOI: 10.4230/LIPIcs.STACS.2024.16

Gapped String Indexing in Subquadratic Space and Sublinear Query Time

Authors: Philip Bille, Inge Li Gørtz, Moshe Lewenstein, Solon P. Pissis, Eva Rotenberg, and Teresa Anna Steiner

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract

In Gapped String Indexing, the goal is to compactly represent a string S of length n such that for any query consisting of two strings P₁ and P₂, called patterns, and an integer interval [α, β], called gap range, we can quickly find occurrences of P₁ and P₂ in S with distance in [α, β]. Gapped String Indexing is a central problem in computational biology and text mining and has thus received significant research interest, including parameterized and heuristic approaches. Despite this interest, the best-known time-space trade-offs for Gapped String Indexing are the straightforward 𝒪(n) space and 𝒪(n+ occ) query time or Ω(n²) space and Õ(|P₁| + |P₂| + occ) query time. We break through this barrier obtaining the first interesting trade-offs with polynomially subquadratic space and polynomially sublinear query time. In particular, we show that, for every 0 ≤ δ ≤ 1, there is a data structure for Gapped String Indexing with either Õ(n^{2-δ/3}) or Õ(n^{3-2δ}) space and Õ(|P₁| + |P₂| + n^{δ}⋅ (occ+1)) query time, where occ is the number of reported occurrences. As a new fundamental tool towards obtaining our main result, we introduce the Shifted Set Intersection problem: preprocess a collection of sets S₁, …, S_k of integers such that for any query consisting of three integers i,j,s, we can quickly output YES if and only if there exist a ∈ S_i and b ∈ S_j with a+s = b. We start by showing that the Shifted Set Intersection problem is equivalent to the indexing variant of 3SUM (3SUM Indexing) [Golovnev et al., STOC 2020]. We then give a data structure for Shifted Set Intersection with gaps, which entails a solution to the Gapped String Indexing problem. Furthermore, we enhance our data structure for deciding Shifted Set Intersection, so that we can support the reporting variant of the problem, i.e., outputting all certificates in the affirmative case. Via the obtained equivalence to 3SUM Indexing, we thus give new improved data structures for the reporting variant of 3SUM Indexing, and we show how this improves upon the state-of-the-art solution for Jumbled Indexing [Chan and Lewenstein, STOC 2015] for any alphabet of constant size σ > 5.

Cite as

Philip Bille, Inge Li Gørtz, Moshe Lewenstein, Solon P. Pissis, Eva Rotenberg, and Teresa Anna Steiner. Gapped String Indexing in Subquadratic Space and Sublinear Query Time. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bille_et_al:LIPIcs.STACS.2024.16,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Lewenstein, Moshe and Pissis, Solon P. and Rotenberg, Eva and Steiner, Teresa Anna},
  title =	{{Gapped String Indexing in Subquadratic Space and Sublinear Query Time}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.16},
  URN =		{urn:nbn:de:0030-drops-197262},
  doi =		{10.4230/LIPIcs.STACS.2024.16},
  annote =	{Keywords: data structures, string indexing, indexing with gaps, two patterns}
}

@InProceedings{bille_et_al:LIPIcs.STACS.2024.16,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Lewenstein, Moshe and Pissis, Solon P. and Rotenberg, Eva and Steiner, Teresa Anna},
  title =	{{Gapped String Indexing in Subquadratic Space and Sublinear Query Time}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.16},
  URN =		{urn:nbn:de:0030-drops-197262},
  doi =		{10.4230/LIPIcs.STACS.2024.16},
  annote =	{Keywords: data structures, string indexing, indexing with gaps, two patterns}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2023.39

Dynamic Planar Embedding Is in DynFO

Authors: Samir Datta, Asif Khan, and Anish Mukherjee

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

Planar Embedding is a drawing of a graph on the plane such that the edges do not intersect each other except at the vertices. We know that testing the planarity of a graph and computing its embedding (if it exists), can efficiently be computed, both sequentially [John E. Hopcroft and Robert Endre Tarjan, 1974] and in parallel [Vijaya Ramachandran and John H. Reif, 1994], when the entire graph is presented as input. In the dynamic setting, the input graph changes one edge at a time through insertion and deletions and planarity testing/embedding has to be updated after every change. By storing auxilliary information we can improve the complexity of dynamic planarity testing/embedding over the obvious recomputation from scratch. In the sequential dynamic setting, there has been a series of works [David Eppstein et al., 1996; Giuseppe F. Italiano et al., 1993; Jacob Holm et al., 2018; Jacob Holm and Eva Rotenberg, 2020], culminating in the breakthrough result of polylog(n) sequential time (amortized) planarity testing algorithm of Holm and Rotenberg [Jacob Holm and Eva Rotenberg, 2020]. In this paper we study planar embedding through the lens of DynFO, a parallel dynamic complexity class introduced by Patnaik et al [Sushant Patnaik and Neil Immerman, 1997] (also [Guozhu Dong et al., 1995]). We show that it is possible to dynamically maintain whether an edge can be inserted to a planar graph without causing non-planarity in DynFO. We extend this to show how to maintain an embedding of a planar graph under both edge insertions and deletions, while rejecting edge insertions that violate planarity. Our main idea is to maintain embeddings of only the triconnected components and a special two-colouring of separating pairs that enables us to side-step cascading flips when embedding of a biconnected planar graph changes, a major issue for sequential dynamic algorithms [Jacob Holm and Eva Rotenberg, 2020; Jacob Holm and Eva Rotenberg, 2020].

Cite as

Samir Datta, Asif Khan, and Anish Mukherjee. Dynamic Planar Embedding Is in DynFO. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{datta_et_al:LIPIcs.MFCS.2023.39,
  author =	{Datta, Samir and Khan, Asif and Mukherjee, Anish},
  title =	{{Dynamic Planar Embedding Is in DynFO}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.39},
  URN =		{urn:nbn:de:0030-drops-185736},
  doi =		{10.4230/LIPIcs.MFCS.2023.39},
  annote =	{Keywords: Dynamic Complexity, Planar graphs, Planar embedding}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2023.13

Multilevel Skeletonization Using Local Separators

Authors: J. Andreas Bærentzen, Rasmus Emil Christensen, Emil Toftegaard Gæde, and Eva Rotenberg

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract

In this paper we give a new, efficient algorithm for computing curve skeletons, based on local separators. Our efficiency stems from a multilevel approach, where we solve small problems across levels of detail and combine these in order to quickly obtain a skeleton. We do this in a highly modular fashion, ensuring complete flexibility in adapting the algorithm for specific types of input or for otherwise targeting specific applications. Separator based skeletonization was first proposed by Bærentzen and Rotenberg in [ACM Tran. Graphics'21], showing high quality output at the cost of running times which become prohibitive for large inputs. Our new approach retains the high quality output, and applicability to any spatially embedded graph, while being orders of magnitude faster for all practical purposes. We test our skeletonization algorithm for efficiency and quality in practice, comparing it to local separator skeletonization on the University of Groningen Skeletonization Benchmark [Telea'16].

Cite as

J. Andreas Bærentzen, Rasmus Emil Christensen, Emil Toftegaard Gæde, and Eva Rotenberg. Multilevel Skeletonization Using Local Separators. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brentzen_et_al:LIPIcs.SoCG.2023.13,
  author =	{B{\ae}rentzen, J. Andreas and Christensen, Rasmus Emil and G{\ae}de, Emil Toftegaard and Rotenberg, Eva},
  title =	{{Multilevel Skeletonization Using Local Separators}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.13},
  URN =		{urn:nbn:de:0030-drops-178637},
  doi =		{10.4230/LIPIcs.SoCG.2023.13},
  annote =	{Keywords: Algorithm engineering, experimentation and implementation, shape skeletonization, curve skeletons, multilevel algorithm}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2023.40

Worst-Case Deterministic Fully-Dynamic Biconnectivity in Changeable Planar Embeddings

Authors: Jacob Holm, Ivor van der Hoog, and Eva Rotenberg

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract

We study dynamic planar graphs with n vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a planar graph, subject to connectivity and 2-vertex-connectivity (biconnectivity) queries between pairs of vertices. Whenever a query pair is connected and not biconnected, we find the first and last cutvertex separating them. Additionally, we allow local changes to the embedding by flipping the embedding of a subgraph that is connected by at most two vertices to the rest of the graph. We support all queries and updates in deterministic, worst-case, O(log² n) time, using an O(n)-sized data structure.

Cite as

Jacob Holm, Ivor van der Hoog, and Eva Rotenberg. Worst-Case Deterministic Fully-Dynamic Biconnectivity in Changeable Planar Embeddings. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{holm_et_al:LIPIcs.SoCG.2023.40,
  author =	{Holm, Jacob and van der Hoog, Ivor and Rotenberg, Eva},
  title =	{{Worst-Case Deterministic Fully-Dynamic Biconnectivity in Changeable Planar Embeddings}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.40},
  URN =		{urn:nbn:de:0030-drops-178909},
  doi =		{10.4230/LIPIcs.SoCG.2023.40},
  annote =	{Keywords: dynamic graphs, planarity, connectivity}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.STACS.2023.2

Amortised Analysis of Dynamic Data Structures (Invited Talk)

Authors: Eva Rotenberg

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

Abstract

In dynamic data structures, one is interested in efficiently facilitating queries to a data set, while being able to efficiently perform updates as the data set undergoes changes. Often, relaxing the efficiency measure to the amortised setting allows for simpler algorithms. A well-known example of a data structure with amortised guarantees is the splay tree by Sleator and Tarjan [Daniel D. Sleator and Robert E. Tarjan, 1985]. Similarly, in data structures for dynamic graphs, one is interested in efficiently maintaining some information about the graph, or facilitating queries, as the graph undergoes changes in the form of insertion and deletion of edges. Examples of such information include connectivity, planarity, and approximate sparsity of the graph: is the graph presently connected? Is it planar? Has its arboricity grossly exceeded some specified number α̃? The related queries could be: is a connected to b? Are the edges uv and uw consecutive in the ordering around u in its current planar embedding? Or, report the O(α) out-edges of vertex x. In this talk, we will see Brodal and Fagerberg’s amortised algorithm for orienting sparse graphs (i.e. of arboricity ≤ α), so that each vertex has O(α) out-edges [Gerth Stølting Brodal and Rolf Fagerberg, 1999]. The algorithm itself is extremely simple, and uses an elegant amortised argument in its analysis. Then, we will visit the problem of dynamic planarity testing: is the graph presently planar? Here, we will see an elegant amortised reduction to the seemingly easier problem, where planarity-violating edges may be detected and rejected [Eppstein et al., 1996]. We will see a sketch of how the current state-of-the-art algorithm for efficient planarity testing [Jacob Holm and Eva Rotenberg, 2020] uses ideas similar to those in [Gerth Stølting Brodal and Rolf Fagerberg, 1999] to analyse the behaviour of a greedy algorithm via a possibly inefficient algorithm with provably low recourse [Jacob Holm and Eva Rotenberg, 2020]. If time permits, we will touch upon a recent simple amortised data structure for maintaining information in dynamic forests [Jacob Holm et al., 2023], which builds on ideas from splay trees. The talk concludes with some open questions in the area.

Cite as

Eva Rotenberg. Amortised Analysis of Dynamic Data Structures (Invited Talk). In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rotenberg:LIPIcs.STACS.2023.2,
  author =	{Rotenberg, Eva},
  title =	{{Amortised Analysis of Dynamic Data Structures}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{2:1--2:2},
  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.2023.2},
  URN =		{urn:nbn:de:0030-drops-176547},
  doi =		{10.4230/LIPIcs.STACS.2023.2},
  annote =	{Keywords: Amortised analysis, splaying, dynamic graphs, planarity testing}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.ESA.2022

LIPIcs, Volume 244, ESA 2022, Complete Volume

Authors: Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman

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

Abstract

LIPIcs, Volume 244, ESA 2022, Complete Volume

Cite as

30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 1-1406, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{chechik_et_al:LIPIcs.ESA.2022,
  title =	{{LIPIcs, Volume 244, ESA 2022, Complete Volume}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{1--1406},
  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},
  URN =		{urn:nbn:de:0030-drops-169374},
  doi =		{10.4230/LIPIcs.ESA.2022},
  annote =	{Keywords: LIPIcs, Volume 244, ESA 2022, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.ESA.2022.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman

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

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 0:i-0:xxii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chechik_et_al:LIPIcs.ESA.2022.0,
  author =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{0:i--0:xxii},
  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.2022.0},
  URN =		{urn:nbn:de:0030-drops-169382},
  doi =		{10.4230/LIPIcs.ESA.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.ESA.2022.1

Enumerating Minimal Connected Dominating Sets

Authors: Faisal N. Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, and Kevin Mann

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

Abstract

The question to enumerate all (inclusion-wise) minimal connected dominating sets in a graph of order n in time significantly less than 2ⁿ is an open question that was asked in many places. We answer this question affirmatively, by providing an enumeration algorithm that runs in time 𝒪(1.9896ⁿ), using polynomial space only. The key to this result is the consideration of this enumeration problem on 2-degenerate graphs, which is proven to be possible in time 𝒪(1.9767ⁿ). Apart from solving this old open question, we also show new lower bound results. More precisely, we construct a family of graphs of order n with Ω(1.4890ⁿ) many minimal connected dominating sets, while previous examples achieved Ω(1.4422ⁿ). Our example happens to yield 4-degenerate graphs. Additionally, we give lower bounds for the previously not considered classes of 2-degenerate and of 3-degenerate graphs, which are Ω(1.3195ⁿ) and Ω(1.4723ⁿ), respectively. We also address essential questions concerning output-sensitive enumeration. Namely, we give reasons why our algorithm cannot be turned into an enumeration algorithm that guarantees polynomial delay without much efforts. More precisely, we prove that it is NP-complete to decide, given a graph G and a vertex set U, if there exists a minimal connected dominating set D with U ⊆ D, even if G is known to be 2-degenerate. Our reduction also shows that even any subexponential delay is not easy to achieve for enumerating minimal connected dominating sets. Another reduction shows that no FPT-algorithms can be expected for this extension problem concerning minimal connected dominating sets, parameterized by |U|. This also adds one more problem to the still rather few natural parameterized problems that are complete for the class W[3]. We also relate our enumeration problem to the famous open Hitting Set Transversal problem, which can be phrased in our context as the question to enumerate all minimal dominating sets of a graph with polynomial delay by showing that a polynomial-delay enumeration algorithm for minimal connected dominating sets implies an affirmative algorithmic solution to the Hitting Set Transversal problem.

Cite as

Faisal N. Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, and Kevin Mann. Enumerating Minimal Connected Dominating Sets. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{abukhzam_et_al:LIPIcs.ESA.2022.1,
  author =	{Abu-Khzam, Faisal N. and Fernau, Henning and Gras, Benjamin and Liedloff, Mathieu and Mann, Kevin},
  title =	{{Enumerating Minimal Connected Dominating Sets}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{1:1--1:15},
  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.2022.1},
  URN =		{urn:nbn:de:0030-drops-169390},
  doi =		{10.4230/LIPIcs.ESA.2022.1},
  annote =	{Keywords: enumeration problems, connected domination, degenerate graphs}
}

Document

DOI: 10.4230/LIPIcs.ESA.2022.2

Non-Adaptive Edge Counting and Sampling via Bipartite Independent Set Queries

Authors: Raghavendra Addanki, Andrew McGregor, and Cameron Musco

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

Abstract

We study the problem of estimating the number of edges in an n-vertex graph, accessed via the Bipartite Independent Set query model introduced by Beame et al. (TALG '20). In this model, each query returns a Boolean, indicating the existence of at least one edge between two specified sets of nodes. We present a non-adaptive algorithm that returns a (1± ε) relative error approximation to the number of edges, with query complexity Õ(ε^{-5}log⁵ n), where Õ(⋅) hides poly(log log n) dependencies. This is the first non-adaptive algorithm in this setting achieving poly(1/ε,log n) query complexity. Prior work requires Ω(log² n) rounds of adaptivity. We avoid this by taking a fundamentally different approach, inspired by work on single-pass streaming algorithms. Moreover, for constant ε, our query complexity significantly improves on the best known adaptive algorithm due to Bhattacharya et al. (STACS '22), which requires O(ε^{-2} log^{11} n) queries. Building on our edge estimation result, we give the first {non-adaptive} algorithm for outputting a nearly uniformly sampled edge with query complexity Õ(ε^{-6} log⁶ n), improving on the works of Dell et al. (SODA '20) and Bhattacharya et al. (STACS '22), which require Ω(log³ n) rounds of adaptivity. Finally, as a consequence of our edge sampling algorithm, we obtain a Õ(n log^8 n) query algorithm for connectivity, using two rounds of adaptivity. This improves on a three-round algorithm of Assadi et al. (ESA '21) and is tight; there is no non-adaptive algorithm for connectivity making o(n²) queries.

Cite as

Raghavendra Addanki, Andrew McGregor, and Cameron Musco. Non-Adaptive Edge Counting and Sampling via Bipartite Independent Set Queries. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{addanki_et_al:LIPIcs.ESA.2022.2,
  author =	{Addanki, Raghavendra and McGregor, Andrew and Musco, Cameron},
  title =	{{Non-Adaptive Edge Counting and Sampling via Bipartite Independent Set Queries}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{2:1--2:16},
  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.2022.2},
  URN =		{urn:nbn:de:0030-drops-169400},
  doi =		{10.4230/LIPIcs.ESA.2022.2},
  annote =	{Keywords: sublinear graph algorithms, bipartite independent set queries, edge sampling and counting, graph connectivity, query adaptivity}
}

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