98 Search Results for "M�ller, Paul"

Document
Extended Abstract
DOI: 10.4230/LIPIcs.TIME.2023.20
Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster (Extended Abstract)

Authors: Luke Hunsberger and Roberto Posenato

Published in: LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

Abstract
In many sectors of real-world industry, it is necessary to plan and schedule tasks allocated to agents participating in complex processes. Temporal planning aims to schedule tasks while respecting temporal constraints such as release times, maximum durations, and deadlines, which requires quantitative temporal reasoning. Over the years, several major application developers have highlighted the need for the explicit representation of actions with uncertain durations; efficient algorithms for determining whether plans involving such actions are controllable; and efficient algorithms for converting such plans into forms that enable them to be executed in real time with minimal computation, while preserving maximum flexibility. A Simple Temporal Network with Uncertainty (STNU) is a data structure for reasoning about time constraints on actions that may have uncertain durations. An STNU is a triple (𝒯, 𝒞, ℒ) where 𝒯 is a set of real-valued variables called timepoints, 𝒞 is a set of constraints of the form Y-X ≤ δ, where X, Y ∈ 𝒯 and δ ∈ 𝐑, and ℒ is a set of contingent links of the form (A,x,y,C), where A,C ∈ 𝒯 and 0 < x < y < ∞. A contingent link (A,x,y,C) represents an uncertain duration where A is the activation timepoint, C is the contingent timepoint, and y-x is the uncertainty in the duration C-A. Typically, an executor controls the execution of A, but only observes the execution of C in real time. Although uncontrollable, the duration is guaranteed to satisfy C-A ∈ [x,y]. We let n = |𝒯|, m = |𝒞| and k = |ℒ|. An STNU graph is a pair (𝒯, ℰ), where the timepoints in 𝒯 serve as nodes in the graph, and the edges in ℰ correspond to the constraints in 𝒞 and contingent links in ℒ. For each Y-X ≤ δ in 𝒞, ℰ contains an ordinary edge X-δ->Y. For each (A,x,y,C) ∈ ℒ, ℰ contains a lower-case (LC) edge, A-c:y->C, and an upper-case (UC) edge, C-C:-y->A, representing the respective possibilities that C-A might take its minimum or maximum value. The LO-edges are the LC or ordinary edges; the OU-edges are the ordinary or UC edges. For any STNU, it is important to determine whether it is dynamically controllable (DC) (i.e., whether it is possible, in real time, to schedule its non-contingent timepoints such that all constraints will necessarily be satisfied no matter what durations turn out for the contingent links). Polynomial-time algorithms are available to solve this DC-checking problem. Each uses rules to generate new edges aiming to bypass certain kinds of edges in the STNU graph. Morris' O(n⁴)-time DC-checking algorithm [Paul Morris, 2006] starts from LC edges, propagating forward along OU-edges, looking for opportunities to generate new OU-edges that bypass the LC edges. Morris' O(n³)-time algorithm [Morris, 2014] starts from negative OU-edges, propagating backward along LO-edges, aiming to bypass negative edges with non-negative edges. The O(mn+k²n + knlog n)-time RUL¯ algorithm [Massimo Cairo et al., 2018] starts from UC edges, propagating backward along LO-edges, aiming to bypass UC edges with ordinary edges. After propagating, each algorithm checks for certain kinds of negative cycles to decide DC-vs.-non-DC. However, being DC only asserts the existence of a dynamic scheduler. It is also crucial to be able to execute a DC STNU efficiently in real time. For maximum flexibility and minimal space and time requirements, a dynamic scheduler for an STNU is typically computed incrementally, in real time, so that it can react to observations of contingent executions as they occur. An efficient dynamic scheduler can be realized by first transforming an STNU into an equivalent dispatchable form [Muscettola et al., 1998; Ioannis Tsamardinos et al., 1998]. Then, to execute the dispatchable STNU, it suffices to maintain time-windows for each timepoint and, as each timepoint X is executed, only updating time-windows for neighbors of X in the graph. Dispatchable STNUs are very important in applications that demand quick responses to observations of contingent events. Of the existing DC-checking algorithms, only Morris' O(n³)-time algorithm necessarily generates a dispatchable STNU for DC inputs. This abstract describes a faster, O(mn + kn² + n² log n)-time algorithm for converting DC STNUs into dispatchable form. (The full journal article is available elsewhere [Luke Hunsberger and Roberto Posenato, 2023].) This improvement is significant for applications (e.g., modeling business processes) where networks are typically sparse. For example, if m = O(n log n) and k = O(log n), then our algorithm runs in O(n²log n) ≪ O(n³) time. Our new Fast Dispatch algorithm, FD_STNU, has three phases. The first phase is similar to the RUL¯ DC-checking algorithm, but generates an order-of-magnitude fewer edges overall, while also generating new UC edges that correspond to wait constraints. The second phase is a version of Morris' 2006 algorithm that propagates forward from LC edges, but only along LO-edges, aiming to generate ordinary bypass edges. The third phase focuses on the subgraph of ordinary edges, which comprise a Simple Temporal Network (STN). It uses an existing dispatchability algorithm for STNs [Ioannis Tsamardinos et al., 1998] to convert that ordinary subgraph into a dispatchable STN. After completing the three phases, the STNU is guaranteed to be dispatchable. We provide the source code of a Java implementation of the considered algorithms (Morris, RUL¯, and FD_STNU) [Posenato, 2022] and the benchmarks used to compare their performances.
Cite as

Luke Hunsberger and Roberto Posenato. Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster (Extended Abstract). In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 20:1-20:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{hunsberger_et_al:LIPIcs.TIME.2023.20,
  author =	{Hunsberger, Luke and Posenato, Roberto},
  title =	{{Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster}},
  booktitle =	{30th International Symposium on Temporal Representation and Reasoning (TIME 2023)},
  pages =	{20:1--20:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-298-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{278},
  editor =	{Artikis, Alexander and Bruse, Florian and Hunsberger, Luke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.20},
  URN =		{urn:nbn:de:0030-drops-191104},
  doi =		{10.4230/LIPIcs.TIME.2023.20},
  annote =	{Keywords: Temporal constraint networks, contingent durations, dispatchable network}
}
Document
Short Paper
DOI: 10.4230/OASIcs.ATMOS.2023.18
Simple Policies for Capacitated Resupply Problems (Short Paper)

Authors: Mette Wagenvoort, Martijn van Ee, Paul Bouman, and Kerry M. Malone

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
We consider the Capacitated Resupply Problem in which locations with a given demand rate should be resupplied by vehicles such that they do not run out of stock and the number of vehicles is minimised. Compared to related problems, we consider the scenario where the payload of the vehicles may not suffice to bring the stock level back to full capacity. We focus on the Homogeneous Capacitated Resupply Problem and present both simple policies that provide 2-approximations and an optimal greedy policy that runs in pseudo-polynomial time.
Cite as

Mette Wagenvoort, Martijn van Ee, Paul Bouman, and Kerry M. Malone. Simple Policies for Capacitated Resupply Problems (Short Paper). In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 18:1-18:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{wagenvoort_et_al:OASIcs.ATMOS.2023.18,
  author =	{Wagenvoort, Mette and van Ee, Martijn and Bouman, Paul and Malone, Kerry M.},
  title =	{{Simple Policies for Capacitated Resupply Problems}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{18:1--18:6},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.18},
  URN =		{urn:nbn:de:0030-drops-187799},
  doi =		{10.4230/OASIcs.ATMOS.2023.18},
  annote =	{Keywords: resupply problems, periodic schedules, approximation guarantee, greedy policy}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.7
Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields

Authors: Russell Impagliazzo, Sasank Mouli, and Toniann Pitassi

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
For every prime p > 0, every n > 0 and κ = O(log n), we show the existence of an unsatisfiable system of polynomial equations over O(n log n) variables of degree O(log n) such that any Polynomial Calculus refutation over 𝔽_p with M extension variables, each depending on at most κ original variables requires size exp(Ω(n²)/10^κ(M + n log n))
Cite as

Russell Impagliazzo, Sasank Mouli, and Toniann Pitassi. Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{impagliazzo_et_al:LIPIcs.CCC.2023.7,
  author =	{Impagliazzo, Russell and Mouli, Sasank and Pitassi, Toniann},
  title =	{{Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.7},
  URN =		{urn:nbn:de:0030-drops-182774},
  doi =		{10.4230/LIPIcs.CCC.2023.7},
  annote =	{Keywords: Proof complexity, Algebraic proof systems, Polynomial Calculus, Extension variables, AC⁰\lbrackp\rbrack-Frege}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.12
Covert Computation in the Abstract Tile-Assembly Model

Authors: Robert M. Alaniz, David Caballero, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
There have been many advances in molecular computation that offer benefits such as targeted drug delivery, nanoscale mapping, and improved classification of nanoscale organisms. This power led to recent work exploring privacy in the computation, specifically, covert computation in self-assembling circuits. Here, we prove several important results related to the concept of a hidden computation in the most well-known model of self-assembly, the Abstract Tile-Assembly Model (aTAM). We show that in 2D, surprisingly, the model is capable of covert computation, but only with an exponential-sized assembly. We also show that the model is capable of covert computation with polynomial-sized assemblies with only one step in the third dimension (just-barely 3D). Finally, we investigate types of functions that can be covertly computed as members of P/Poly.
Cite as

Robert M. Alaniz, David Caballero, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Covert Computation in the Abstract Tile-Assembly Model. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{alaniz_et_al:LIPIcs.SAND.2023.12,
  author =	{Alaniz, Robert M. and Caballero, David and Gomez, Timothy and Grizzell, Elise and Rodriguez, Andrew and Schweller, Robert and Wylie, Tim},
  title =	{{Covert Computation in the Abstract Tile-Assembly Model}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.12},
  URN =		{urn:nbn:de:0030-drops-179482},
  doi =		{10.4230/LIPIcs.SAND.2023.12},
  annote =	{Keywords: self-assembly, covert computation, atam}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.52
Reconstructing Words Using Queries on Subwords or Factors

Authors: Gwenaël Richomme and Matthieu Rosenfeld

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

Abstract
We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k²√{nlog₂(n)}) words. Two previous upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.
Cite as

Gwenaël Richomme and Matthieu Rosenfeld. Reconstructing Words Using Queries on Subwords or Factors. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{richomme_et_al:LIPIcs.STACS.2023.52,
  author =	{Richomme, Gwena\"{e}l and Rosenfeld, Matthieu},
  title =	{{Reconstructing Words Using Queries on Subwords or Factors}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{52:1--52:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.52},
  URN =		{urn:nbn:de:0030-drops-177041},
  doi =		{10.4230/LIPIcs.STACS.2023.52},
  annote =	{Keywords: Word reconstruction, Subwords, Factors}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.WABI.2022.1
Efficient Solutions to Biological Problems Using de Bruijn Graphs (Invited Talk)

Authors: Leena Salmela

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract
The de Bruijn graph has become a standard method in the analysis of sequencing reads in computational biology due to its ability to represent the information contained in large read sets in small space. A de Bruijn graph represents a set of sequencing reads by its k-mers, i.e. the set of substrings of length k that occur in the reads. In the classical definition, the k-mers are the edges of the graph and the nodes are the k-1 bases long prefixes and suffixes of the k-mers. Usually only k-mers occurring several times in the read set are kept to filter out noise in the data. De Bruijn graphs have been used to solve many problems in computational biology including genome assembly [Ramana M. Idury and Michael S. Waterman, 1995; Pavel A. Pevzner et al., 2001; Anton Bankevich et al., 2012; Yu Peng et al., 2010], sequencing error correction [Leena Salmela and Eric Rivals, 2014; Giles Miclotte et al., 2016; Leena Salmela et al., 2017; Limasset et al., 2019], reference free variant calling [Raluca Uricaru et al., 2015], indexing read sets [Camille Marchet et al., 2021], and so on. Next I will discuss two of these problems in more depth. The de Bruijn graph first emerged in computation biology in the context of genome assembly [Ramana M. Idury and Michael S. Waterman, 1995; Pavel A. Pevzner et al., 2001] where the task is to reconstruct a genome based on sequencing reads. As the de Bruijn graph can represent large read sets compactly, it became the standard approach to assemble short reads [Anton Bankevich et al., 2012; Yu Peng et al., 2010]. In the theoretical framework of de Bruijn graph based genome assembly, a genome is thought to be the Eulerian path in the de Bruijn graph built on the sequencing reads. In practise, the Eulerian path is not unique and thus not useful in the biological context. Therefore, practical implementations report subpaths that are guaranteed to be part of any Eulerian path and thus part of the actual genome. Such models include unitigs, which are nonbranching paths of the de Bruijn graph, and more involved definitions such as omnitigs [Alexandru I. Tomescu and Paul Medvedev, 2017]. In genome assembly the choice of k is a crucial matter. A small k can result in a tangled graph, whereas a too large k will fragment the graph. Furthermore, a different value of k may be optimal for different parts of the genome. Variable order de Bruijn graphs [Christina Boucher et al., 2015; Djamal Belazzougui et al., 2016], which represent de Bruijn graphs of all orders k in a single data structure, have been proposed as a solution but no rigorous definition corresponding to unitigs has been presented. We give the first definition of assembled sequences, i.e. contigs, on such graphs and an algorithm for enumerating them. Another problem that can be solved with de Bruijn graphs is the correction of sequencing errors [Leena Salmela and Eric Rivals, 2014; Giles Miclotte et al., 2016; Leena Salmela et al., 2017; Limasset et al., 2019]. Because each position of a genome is sequenced several times, it is possible to correct sequencing errors in reads if we can identify data originating from the same genomic region. A de Bruijn graph can be used to represent compactly the reliable information and the individual reads can be corrected by aligning them to the graph.
Cite as

Leena Salmela. Efficient Solutions to Biological Problems Using de Bruijn Graphs (Invited Talk). In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{salmela:LIPIcs.WABI.2022.1,
  author =	{Salmela, Leena},
  title =	{{Efficient Solutions to Biological Problems Using de Bruijn Graphs}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.1},
  URN =		{urn:nbn:de:0030-drops-170357},
  doi =		{10.4230/LIPIcs.WABI.2022.1},
  annote =	{Keywords: de Bruijn graph, variable order de Bruijn graph, genome assembly, sequencing error correction, k-mers}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.79
On Extended Boundary Sequences of Morphic and Sturmian Words

Authors: Michel Rigo, Manon Stipulanti, and Markus A. Whiteland

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the nth term of the 𝓁-boundary sequence of an infinite word is the finite set of pairs (u,v) of prefixes and suffixes of length 𝓁 appearing in factors uyv of length n+𝓁 (n ≥ 𝓁 ≥ 1). Otherwise stated, for increasing values of n, one looks for all pairs of factors of length 𝓁 separated by n-𝓁 symbols. For the large class of addable numeration systems U, we show that if an infinite word is U-automatic, then the same holds for its 𝓁-boundary sequence. In particular, they are both morphic (or generated by an HD0L system). We also provide examples of numeration systems and U-automatic words with a boundary sequence that is not U-automatic. In the second part of the paper, we study the 𝓁-boundary sequence of a Sturmian word. We show that it is obtained through a sliding block code from the characteristic Sturmian word of the same slope. We also show that it is the image under a morphism of some other characteristic Sturmian word.
Cite as

Michel Rigo, Manon Stipulanti, and Markus A. Whiteland. On Extended Boundary Sequences of Morphic and Sturmian Words. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{rigo_et_al:LIPIcs.MFCS.2022.79,
  author =	{Rigo, Michel and Stipulanti, Manon and Whiteland, Markus A.},
  title =	{{On Extended Boundary Sequences of Morphic and Sturmian Words}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{79:1--79:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.79},
  URN =		{urn:nbn:de:0030-drops-168776},
  doi =		{10.4230/LIPIcs.MFCS.2022.79},
  annote =	{Keywords: Boundary sequences, Sturmian words, Numeration systems, Automata, Graph of addition}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.49
Dynamic Connectivity in Disk Graphs

Authors: Haim Kaplan, Alexander Kauer, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty, and Paul Seiferth

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Let S ⊆ ℝ² be a set of n planar sites, such that each s ∈ S has an associated radius r_s > 0. Let 𝒟(S) be the disk intersection graph for S. It has vertex set S and an edge between two distinct sites s, t ∈ S if and only if the disks with centers s, t and radii r_s, r_t intersect. Our goal is to design data structures that maintain the connectivity structure of 𝒟(S) as sites are inserted and/or deleted. First, we consider unit disk graphs, i.e., r_s = 1, for all s ∈ S. We describe a data structure that has O(log² n) amortized update and O(log n/log log n) amortized query time. Second, we look at disk graphs with bounded radius ratio Ψ, i.e., for all s ∈ S, we have 1 ≤ r_s ≤ Ψ, for a Ψ ≥ 1 known in advance. In the fully dynamic case, we achieve amortized update time O(Ψ λ₆(log n) log⁷ n) and query time O(log n/log log n), where λ_s(n) is the maximum length of a Davenport-Schinzel sequence of order s on n symbols. In the incremental case, where only insertions are allowed, we get logarithmic dependency on Ψ, with O(α(n)) query time and O(logΨ λ₆(log n) log⁷ n) update time. For the decremental setting, where only deletions are allowed, we first develop an efficient disk revealing structure: given two sets R and B of disks, we can delete disks from R, and upon each deletion, we receive a list of all disks in B that no longer intersect the union of R. Using this, we get decremental data structures with amortized query time O(log n/log log n) that support m deletions in O((nlog⁵ n + m log⁷ n) λ₆(log n) + nlog Ψ log⁴n) overall time for bounded radius ratio Ψ and O((nlog⁶ n + m log⁸n) λ₆(log n)) for arbitrary radii.
Cite as

Haim Kaplan, Alexander Kauer, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty, and Paul Seiferth. Dynamic Connectivity in Disk Graphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 49:1-49:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{kaplan_et_al:LIPIcs.SoCG.2022.49,
  author =	{Kaplan, Haim and Kauer, Alexander and Klost, Katharina and Knorr, Kristin and Mulzer, Wolfgang and Roditty, Liam and Seiferth, Paul},
  title =	{{Dynamic Connectivity in Disk Graphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{49:1--49:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.49},
  URN =		{urn:nbn:de:0030-drops-160572},
  doi =		{10.4230/LIPIcs.SoCG.2022.49},
  annote =	{Keywords: Disk Graphs, Connectivity, Lower Envelopes}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.18
Fully Dynamic Four-Vertex Subgraph Counting

Authors: Kathrin Hanauer, Monika Henzinger, and Qi Cheng Hua

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic amortized O(m^{1/2}) update time, and any other connected four-vertex subgraph which is not a clique in deterministic amortized update time O(m^{2/3}). Queries can be answered in constant time. We also study the query times for subgraphs containing an arbitrary edge that is supplied only with the query as well as the case where only subgraphs containing a vertex s that is fixed beforehand are considered. For length-3 paths, paws, 4-cycles, and diamonds our bounds match or are not far from (conditional) lower bounds: Based on the OMv conjecture we show that any dynamic algorithm that detects the existence of paws, diamonds, or 4-cycles or that counts length-3 paths takes update time Ω(m^{1/2-δ}). Additionally, for 4-cliques and all connected induced subgraphs, we show a lower bound of Ω(m^{1-δ}) for any small constant δ > 0 for the amortized update time, assuming the static combinatorial 4-clique conjecture holds. This shows that the O(m) algorithm by Eppstein et al. [David Eppstein et al., 2012] for these subgraphs cannot be improved by a polynomial factor.
Cite as

Kathrin Hanauer, Monika Henzinger, and Qi Cheng Hua. Fully Dynamic Four-Vertex Subgraph Counting. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{hanauer_et_al:LIPIcs.SAND.2022.18,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Hua, Qi Cheng},
  title =	{{Fully Dynamic Four-Vertex Subgraph Counting}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.18},
  URN =		{urn:nbn:de:0030-drops-159608},
  doi =		{10.4230/LIPIcs.SAND.2022.18},
  annote =	{Keywords: Dynamic Graph Algorithms, Subgraph Counting, Motif Search}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.28
MAX CUT in Weighted Random Intersection Graphs and Discrepancy of Sparse Random Set Systems

Authors: Sotiris Nikoletseas, Christoforos Raptopoulos, and Paul Spirakis

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

Abstract
Let V be a set of n vertices, M a set of m labels, and let 𝐑 be an m × n matrix of independent Bernoulli random variables with probability of success p; columns of 𝐑 are incidence vectors of label sets assigned to vertices. A random instance G(V, E, 𝐑^T 𝐑) of the weighted random intersection graph model is constructed by drawing an edge with weight equal to the number of common labels (namely [𝐑^T 𝐑]_{v,u}) between any two vertices u, v for which this weight is strictly larger than 0. In this paper we study the average case analysis of Weighted Max Cut, assuming the input is a weighted random intersection graph, i.e. given G(V, E, 𝐑^T 𝐑) we wish to find a partition of V into two sets so that the total weight of the edges having exactly one endpoint in each set is maximized. In particular, we initially prove that the weight of a maximum cut of G(V, E, 𝐑^T 𝐑) is concentrated around its expected value, and then show that, when the number of labels is much smaller than the number of vertices (in particular, m = n^α, α < 1), a random partition of the vertices achieves asymptotically optimal cut weight with high probability. Furthermore, in the case n = m and constant average degree (i.e. p = Θ(1)/n), we show that with high probability, a majority type randomized algorithm outputs a cut with weight that is larger than the weight of a random cut by a multiplicative constant strictly larger than 1. Then, we formally prove a connection between the computational problem of finding a (weighted) maximum cut in G(V, E, 𝐑^T 𝐑) and the problem of finding a 2-coloring that achieves minimum discrepancy for a set system Σ with incidence matrix 𝐑 (i.e. minimum imbalance over all sets in Σ). We exploit this connection by proposing a (weak) bipartization algorithm for the case m = n, p = Θ(1)/n that, when it terminates, its output can be used to find a 2-coloring with minimum discrepancy in a set system with incidence matrix 𝐑. In fact, with high probability, the latter 2-coloring corresponds to a bipartition with maximum cut-weight in G(V, E, 𝐑^T 𝐑). Finally, we prove that our (weak) bipartization algorithm terminates in polynomial time, with high probability, at least when p = c/n, c < 1.
Cite as

Sotiris Nikoletseas, Christoforos Raptopoulos, and Paul Spirakis. MAX CUT in Weighted Random Intersection Graphs and Discrepancy of Sparse Random Set Systems. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{nikoletseas_et_al:LIPIcs.ISAAC.2021.28,
  author =	{Nikoletseas, Sotiris and Raptopoulos, Christoforos and Spirakis, Paul},
  title =	{{MAX CUT in Weighted Random Intersection Graphs and Discrepancy of Sparse Random Set Systems}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.28},
  URN =		{urn:nbn:de:0030-drops-154612},
  doi =		{10.4230/LIPIcs.ISAAC.2021.28},
  annote =	{Keywords: Random Intersection Graphs, Maximum Cut, Discrepancy}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2021.10
Multiparty Session Types for Safe Runtime Adaptation in an Actor Language

Authors: Paul Harvey, Simon Fowler, Ornela Dardha, and Simon J. Gay

Published in: LIPIcs, Volume 194, 35th European Conference on Object-Oriented Programming (ECOOP 2021)

Abstract
Human fallibility, unpredictable operating environments, and the heterogeneity of hardware devices are driving the need for software to be able to adapt as seen in the Internet of Things or telecommunication networks. Unfortunately, mainstream programming languages do not readily allow a software component to sense and respond to its operating environment, by discovering, replacing, and communicating with components that are not part of the original system design, while maintaining static correctness guarantees. In particular, if a new component is discovered at runtime, there is no guarantee that its communication behaviour is compatible with existing components. We address this problem by using multiparty session types with explicit connection actions, a type formalism used to model distributed communication protocols. By associating session types with software components, the discovery process can check protocol compatibility and, when required, correctly replace components without jeopardising safety. We present the design and implementation of EnsembleS, the first actor-based language with adaptive features and a static session type system, and apply it to a case study based on an adaptive DNS server. We formalise the type system of EnsembleS and prove the safety of well-typed programs, making essential use of recent advances in non-classical multiparty session types.
Cite as

Paul Harvey, Simon Fowler, Ornela Dardha, and Simon J. Gay. Multiparty Session Types for Safe Runtime Adaptation in an Actor Language. In 35th European Conference on Object-Oriented Programming (ECOOP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 194, pp. 10:1-10:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{harvey_et_al:LIPIcs.ECOOP.2021.10,
  author =	{Harvey, Paul and Fowler, Simon and Dardha, Ornela and Gay, Simon J.},
  title =	{{Multiparty Session Types for Safe Runtime Adaptation in an Actor Language}},
  booktitle =	{35th European Conference on Object-Oriented Programming (ECOOP 2021)},
  pages =	{10:1--10:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-190-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{194},
  editor =	{M{\o}ller, Anders and Sridharan, Manu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2021.10},
  URN =		{urn:nbn:de:0030-drops-140539},
  doi =		{10.4230/LIPIcs.ECOOP.2021.10},
  annote =	{Keywords: Concurrency, session types, adaptation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2021.1
Duality in Action (Invited Talk)

Authors: Paul Downen and Zena M. Ariola

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
The duality between "true" and "false" is a hallmark feature of logic. We show how this duality can be put to use in the theory and practice of programming languages and their implementations, too. Starting from a foundation of constructive logic as dialogues, we illustrate how it describes a symmetric language for computation, and survey several applications of the dualities found therein.
Cite as

Paul Downen and Zena M. Ariola. Duality in Action (Invited Talk). In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 1:1-1:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{downen_et_al:LIPIcs.FSCD.2021.1,
  author =	{Downen, Paul and Ariola, Zena M.},
  title =	{{Duality in Action}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{1:1--1:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.1},
  URN =		{urn:nbn:de:0030-drops-142390},
  doi =		{10.4230/LIPIcs.FSCD.2021.1},
  annote =	{Keywords: Duality, Logic, Curry-Howard, Sequent Calculus, Rewriting, Compilation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.9
Tight Approximation Guarantees for Concave Coverage Problems

Authors: Siddharth Barman, Omar Fawzi, and Paul Fermé

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
In the maximum coverage problem, we are given subsets T_1, …, T_m of a universe [n] along with an integer k and the objective is to find a subset S ⊆ [m] of size k that maximizes C(S) : = |⋃_{i ∈ S} T_i|. It is a classic result that the greedy algorithm for this problem achieves an optimal approximation ratio of 1-e^{-1}. In this work we consider a generalization of this problem wherein an element a can contribute by an amount that depends on the number of times it is covered. Given a concave, nondecreasing function φ, we define C^{φ}(S) := ∑_{a ∈ [n]}w_aφ(|S|_a), where |S|_a = |{i ∈ S : a ∈ T_i}|. The standard maximum coverage problem corresponds to taking φ(j) = min{j,1}. For any such φ, we provide an efficient algorithm that achieves an approximation ratio equal to the Poisson concavity ratio of φ, defined by α_{φ} : = min_{x ∈ ℕ^*} 𝔼[φ(Poi(x))] / φ(𝔼[Poi(x)]). Complementing this approximation guarantee, we establish a matching NP-hardness result when φ grows in a sublinear way. As special cases, we improve the result of [Siddharth Barman et al., 2020] about maximum multi-coverage, that was based on the unique games conjecture, and we recover the result of [Szymon Dudycz et al., 2020] on multi-winner approval-based voting for geometrically dominant rules. Our result goes beyond these special cases and we illustrate it with applications to distributed resource allocation problems, welfare maximization problems and approval-based voting for general rules.
Cite as

Siddharth Barman, Omar Fawzi, and Paul Fermé. Tight Approximation Guarantees for Concave Coverage Problems. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{barman_et_al:LIPIcs.STACS.2021.9,
  author =	{Barman, Siddharth and Fawzi, Omar and Ferm\'{e}, Paul},
  title =	{{Tight Approximation Guarantees for Concave Coverage Problems}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.9},
  URN =		{urn:nbn:de:0030-drops-136543},
  doi =		{10.4230/LIPIcs.STACS.2021.9},
  annote =	{Keywords: Approximation Algorithms, Coverage Problems, Concave Function}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.23
One-Tape Turing Machine and Branching Program Lower Bounds for MCSP

Authors: Mahdi Cheraghchi, Shuichi Hirahara, Dimitrios Myrisiotis, and Yuichi Yoshida

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
For a size parameter s: ℕ → ℕ, the Minimum Circuit Size Problem (denoted by MCSP[s(n)]) is the problem of deciding whether the minimum circuit size of a given function f : {0,1}ⁿ → {0,1} (represented by a string of length N : = 2ⁿ) is at most a threshold s(n). A recent line of work exhibited "hardness magnification" phenomena for MCSP: A very weak lower bound for MCSP implies a breakthrough result in complexity theory. For example, McKay, Murray, and Williams (STOC 2019) implicitly showed that, for some constant μ₁ > 0, if MCSP[2^{μ₁⋅ n}] cannot be computed by a one-tape Turing machine (with an additional one-way read-only input tape) running in time N^{1.01}, then P≠NP. In this paper, we present the following new lower bounds against one-tape Turing machines and branching programs: 1) A randomized two-sided error one-tape Turing machine (with an additional one-way read-only input tape) cannot compute MCSP[2^{μ₂⋅n}] in time N^{1.99}, for some constant μ₂ > μ₁. 2) A non-deterministic (or parity) branching program of size o(N^{1.5}/log N) cannot compute MKTP, which is a time-bounded Kolmogorov complexity analogue of MCSP. This is shown by directly applying the Nečiporuk method to MKTP, which previously appeared to be difficult. 3) The size of any non-deterministic, co-non-deterministic, or parity branching program computing MCSP is at least N^{1.5-o(1)}. These results are the first non-trivial lower bounds for MCSP and MKTP against one-tape Turing machines and non-deterministic branching programs, and essentially match the best-known lower bounds for any explicit functions against these computational models. The first result is based on recent constructions of pseudorandom generators for read-once oblivious branching programs (ROBPs) and combinatorial rectangles (Forbes and Kelley, FOCS 2018; Viola 2019). En route, we obtain several related results: 1) There exists a (local) hitting set generator with seed length Õ(√N) secure against read-once polynomial-size non-deterministic branching programs on N-bit inputs. 2) Any read-once co-non-deterministic branching program computing MCSP must have size at least 2^Ω̃(N).
Cite as

Mahdi Cheraghchi, Shuichi Hirahara, Dimitrios Myrisiotis, and Yuichi Yoshida. One-Tape Turing Machine and Branching Program Lower Bounds for MCSP. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{cheraghchi_et_al:LIPIcs.STACS.2021.23,
  author =	{Cheraghchi, Mahdi and Hirahara, Shuichi and Myrisiotis, Dimitrios and Yoshida, Yuichi},
  title =	{{One-Tape Turing Machine and Branching Program Lower Bounds for MCSP}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.23},
  URN =		{urn:nbn:de:0030-drops-136681},
  doi =		{10.4230/LIPIcs.STACS.2021.23},
  annote =	{Keywords: Minimum Circuit Size Problem, Kolmogorov Complexity, One-Tape Turing Machines, Branching Programs, Lower Bounds, Pseudorandom Generators, Hitting Set Generators}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.64
A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth

Authors: Mamadou Moustapha Kanté, Christophe Paul, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels (represented by a graph) that is contaminated by some infectious substance and we are looking for a search strategy that, at each step, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneously occupied by searchers. It was proved that the minimum number of searchers required for a successful cleaning strategy is equal to the pathwidth of the graph plus one. Two desired characteristics for a cleaning strategy is to be monotone (no recontamination occurs) and connected (clean territories always remain connected). Under these two demands, the number of searchers is equivalent to a variant of pathwidth called connected pathwidth. We prove that connected pathwidth is fixed parameter tractable, in particular we design a 2^O(k²)⋅n time algorithm that checks whether the connected pathwidth of G is at most k. This resolves an open question by [Dereniowski, Osula, and Rzążewski, Finding small-width connected path-decompositions in polynomial time. Theor. Comput. Sci., 794:85–100, 2019]. For our algorithm, we enrich the typical sequence technique that is able to deal with the connectivity demand. Typical sequences have been introduced in [Bodlaender and Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358–402, 1996] for the design of linear parameterized algorithms for treewidth and pathwidth. While this technique has been later applied to other parameters, none of its advancements was able to deal with the connectivity demand, as it is a "global" demand that concerns an unbounded number of parts of the graph of unbounded size. The proposed extension is based on an encoding of the connectivity property that is quite versatile and may be adapted so to deliver linear parameterized algorithms for the connected variants of other width parameters as well. An immediate consequence of our result is a 2^O(k²)⋅n time algorithm for the monotone and connected version of the edge search number.
Cite as

Mamadou Moustapha Kanté, Christophe Paul, and Dimitrios M. Thilikos. A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{kante_et_al:LIPIcs.ESA.2020.64,
  author =	{Kant\'{e}, Mamadou Moustapha and Paul, Christophe and Thilikos, Dimitrios M.},
  title =	{{A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.64},
  URN =		{urn:nbn:de:0030-drops-129307},
  doi =		{10.4230/LIPIcs.ESA.2020.64},
  annote =	{Keywords: Graph decompositions, Parameterized algorithms, Typical sequences, Pathwidth, Graph searching}
}
  • Refine by Author
  • 8 Thilikos, Dimitrios M.
  • 5 Paul, Christophe
  • 4 Sau, Ignasi
  • 3 Jansen, Bart M. P.
  • 3 Stull, Donald M.
  • Show More...

  • Refine by Classification
  • 11 Mathematics of computing → Graph algorithms
  • 9 Theory of computation → Graph algorithms analysis
  • 9 Theory of computation → Parameterized complexity and exact algorithms
  • 6 Theory of computation → Design and analysis of algorithms
  • 6 Theory of computation → Fixed parameter tractability
  • Show More...

  • Refine by Keyword
  • 4 treewidth
  • 3 Kolmogorov complexity
  • 3 dynamic programming
  • 3 fixed-parameter tractability
  • 3 lower bounds
  • Show More...

  • Refine by Type
  • 98 document

  • Refine by Publication Year
  • 32 2019
  • 19 2018
  • 16 2020
  • 6 2006
  • 5 2021
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact