123 Search Results for "G�lz, Paul"

Document
DOI: 10.4230/LIPIcs.STACS.2024.55
Tree-Layout Based Graph Classes: Proper Chordal Graphs

Authors: Christophe Paul and Evangelos Protopapas

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

Abstract
Many important graph classes are characterized by means of layouts (a vertex ordering) excluding some patterns. For example, a graph G = (V,E) is a proper interval graph if and only if G has a layout 𝐋 such that for every triple of vertices such that x≺_𝐋 y≺_𝐋 z, if xz ∈ E, then xy ∈ E and yz ∈ E. Such a triple x, y, z is called an indifference triple. In this paper, we investigate the concept of excluding a set of patterns in tree-layouts rather than layouts. A tree-layout 𝐓_G = (T,r,ρ_G) of a graph G = (V,E) is a tree T rooted at some node r and equipped with a one-to-one mapping ρ_G between V and the nodes of T such that for every edge xy ∈ E, either x is an ancestor of y, denoted x≺_{𝐓_G} y, or y is an ancestor of x. Excluding patterns in a tree-layout is now defined using the ancestor relation. This leads to an unexplored territory of graph classes. In this paper, we initiate the study of such graph classes with the class of proper chordal graphs defined by excluding indifference triples in tree-layouts. Our results combine characterization, compact and canonical representation as well as polynomial time algorithms for the recognition and the graph isomorphism of proper chordal graphs. For this, one of the key ingredients is the introduction of the concept of FPQ-hierarchy generalizing the celebrated PQ-tree data-structure.
Cite as

Christophe Paul and Evangelos Protopapas. Tree-Layout Based Graph Classes: Proper Chordal Graphs. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{paul_et_al:LIPIcs.STACS.2024.55,
  author =	{Paul, Christophe and Protopapas, Evangelos},
  title =	{{Tree-Layout Based Graph Classes: Proper Chordal Graphs}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{55:1--55:18},
  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.2024.55},
  URN =		{urn:nbn:de:0030-drops-197652},
  doi =		{10.4230/LIPIcs.STACS.2024.55},
  annote =	{Keywords: Graph classes, Graph representation, Graph isomorphism}
}
Document
DOI: 10.4230/LIPIcs.DNA.29.1
Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer

Authors: Ahmed Shalaby, Chris Thachuk, and Damien Woods

Published in: LIPIcs, Volume 276, 29th International Conference on DNA Computing and Molecular Programming (DNA 29) (2023)

Abstract
Polynomial time dynamic programming algorithms play a crucial role in the design, analysis and engineering of nucleic acid systems including DNA computers and DNA/RNA nanostructures. However, in complex multistranded or pseudoknotted systems, computing the minimum free energy (MFE), and partition function of nucleic acid systems is NP-hard. Despite this, multistranded and/or pseudoknotted systems represent some of the most utilised and successful systems in the field. This leaves open the tempting possibility that many of the kinds of multistranded and/or pseudoknotted systems we wish to engineer actually fall into restricted classes, that do in fact have polynomial time algorithms, but we've just not found them yet. Here, we give polynomial time algorithms for MFE and partition function calculation for a restricted kind of multistranded system called the 1D scaffolded DNA computer. This model of computation thermodynamically favours correct outputs over erroneous states, simulates finite state machines in 1D and Boolean circuits in 2D, and is amenable to DNA storage applications. In an effort to begin to ask the question of whether we can naturally compare the expressivity of nucleic acid systems based on the computational complexity of prediction of their preferred energetic states, we show our MFE problem is in logspace (the complexity class L), making it perhaps one of the simplest known, natural, nucleic acid MFE problems. Finally, we provide a stochastic kinetic simulator for the 1D scaffolded DNA computer and evaluate strategies for efficiently speeding up this thermodynamically favourable system in a constant-temperature kinetic regime.
Cite as

Ahmed Shalaby, Chris Thachuk, and Damien Woods. Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shalaby_et_al:LIPIcs.DNA.29.1,
  author =	{Shalaby, Ahmed and Thachuk, Chris and Woods, Damien},
  title =	{{Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-297-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{276},
  editor =	{Chen, Ho-Lin and Evans, Constantine G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.29.1},
  URN =		{urn:nbn:de:0030-drops-187840},
  doi =		{10.4230/LIPIcs.DNA.29.1},
  annote =	{Keywords: thermodynamic computation, model of computation, molecular computing, minimum free energy, partition function, DNA computing, DNA self-assembly, DNA strand displacement, kinetics simulation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2023.5
Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk)

Authors: Nina Klobas, George B. Mertzios, and Paul G. Spirakis

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

Abstract
Graphs are fundamental tools for modelling relations among objects in various scientific fields. However, traditional static graphs have limitations when it comes to capturing the dynamic nature of real-world systems. To overcome this limitation, temporal graphs have been introduced as a framework to model graphs that change over time. In temporal graphs the edges among vertices appear and disappear at specific time steps, reflecting the temporal dynamics of the observed system, which allows us to analyse time dependent patterns and processes. In this paper we focus on the research related to sliding time windows in temporal graphs. Sliding time windows offer a way to analyse specific time intervals within the lifespan of a temporal graph. By sliding the window along the timeline, we can examine the graph’s characteristics and properties within different time periods. This paper provides an overview of the research on sliding time windows in temporal graphs. Although progress has been made in this field, there are still many interesting questions and challenges to be explored. We discuss some of the open problems and highlight their potential for future research.
Cite as

Nina Klobas, George B. Mertzios, and Paul G. Spirakis. Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{klobas_et_al:LIPIcs.MFCS.2023.5,
  author =	{Klobas, Nina and Mertzios, George B. and Spirakis, Paul G.},
  title =	{{Sliding into the Future: Investigating Sliding Windows in Temporal Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{5:1--5:12},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-185397},
  doi =		{10.4230/LIPIcs.MFCS.2023.5},
  annote =	{Keywords: Temporal Graphs, Sliding Time Windows}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2023.1
A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk)

Authors: Anna R. Karlin

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

Abstract
We describe recent joint work with Nathan Klein and Shayan Oveis Gharan showing that for any metric TSP instance, the max entropy algorithm studied by [Anna R. Karlin et al., 2021] returns a solution of expected cost at most 3/2-ε times the cost of the optimal solution to the subtour elimination LP and hence is a 3/2-ε approximation for the metric TSP problem. The research discussed comes from [Anna R. Karlin et al., 2021], [Anna R. Karlin et al., 2022] and [Anna R. Karlin et al., 2022].
Cite as

Anna R. Karlin. A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{karlin:LIPIcs.ICALP.2023.1,
  author =	{Karlin, Anna R.},
  title =	{{A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.1},
  URN =		{urn:nbn:de:0030-drops-180531},
  doi =		{10.4230/LIPIcs.ICALP.2023.1},
  annote =	{Keywords: Traveling Salesperson Problem, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.1
Snapshot Disjointness in Temporal Graphs

Authors: Allen Ibiapina and Ana Silva

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

Abstract
In the study of temporal graphs, only paths respecting the flow of time are relevant. In this context, many concepts of walks disjointness have been proposed over the years, and the validity of Menger’s Theorem, as well as the complexity of related problems, has been investigated. Menger’s Theorem states that the maximum number of disjoint paths between two vertices is equal to the minimum number of vertices required to disconnect them. In this paper, we introduce and investigate a type of disjointness that is only time dependent. Two walks are said to be snapshot disjoint if they are not active in a same snapshot (also called timestep). The related paths and cut problems are then defined and proved to be W[1]-hard and XP-time solvable when parameterized by the size of the solution. Additionally, in the light of the definition of Mengerian graphs given by Kempe, Kleinberg and Kumar in their seminal paper (STOC'2000), we define a Mengerian graph for time as a graph G for which there is no time labeling for its edges where Menger’s Theorem does not hold in the context of snapshot disjointness. We then give a characterization of Mengerian graphs in terms of forbidden structures and provide a polynomial-time recognition algorithm. Finally, we also prove that, given a temporal graph (G,λ) and a pair of vertices s,z ∈ V(G), deciding whether at most h multiedges can separate s from z is NP-complete, where one multiedge uv is the set of all edges with endpoints u and v.
Cite as

Allen Ibiapina and Ana Silva. Snapshot Disjointness in Temporal Graphs. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ibiapina_et_al:LIPIcs.SAND.2023.1,
  author =	{Ibiapina, Allen and Silva, Ana},
  title =	{{Snapshot Disjointness in Temporal Graphs}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{1:1--1:20},
  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.2023.1},
  URN =		{urn:nbn:de:0030-drops-179379},
  doi =		{10.4230/LIPIcs.SAND.2023.1},
  annote =	{Keywords: Temporal graphs, Menger’s Theorem, Snapshot disjointness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.2
Partial Gathering of Mobile Agents in Dynamic Tori

Authors: Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, and Yonghwan Kim

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

Abstract
In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic tori. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all k agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer g (< k), that agents terminate in a configuration such that either at least g agents or no agent exists at each node. So far, in almost cases, the partial gathering problem has been considered in static graphs. As only one exception, it is considered in a kind of dynamic rings called 1-interval connected rings, that is, one of the links in the ring may be missing at each time step. In this paper, we consider partial gathering in another dynamic topology. Concretely, we consider it in n× n dynamic tori such that each of row rings and column rings is represented as a 1-interval connected ring. In such networks, when k = O(gn), focusing on the relationship between the values of k, n, and g, we aim to characterize the solvability of the partial gathering problem and analyze the move complexity of the proposed algorithms when the problem can be solved. First, we show that agents cannot solve the problem when k = o(gn), which means that Ω (gn) agents are necessary to solve the problem. Second, we show that the problem can be solved with the total number of O(gn³) moves when 2gn+2n-1 ≤ k ≤ 2gn + 6n +16g -12. Finally, we show that the problem can be solved with the total number of O(gn²) moves when k ≥ 2gn + 6n +16g -11. From these results, we show that our algorithms can solve the partial gathering problem in dynamic tori with the asymptotically optimal number Θ (gn) of agents. In addition, we show that agents require a total number of Ω(gn²) moves to solve the partial gathering problem in dynamic tori when k = Θ(gn). Thus, when k ≥ 2gn+6n+16g -11, our algorithm can solve the problem with asymptotically optimal number O(gn²) of agent moves.
Cite as

Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, and Yonghwan Kim. Partial Gathering of Mobile Agents in Dynamic Tori. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shibata_et_al:LIPIcs.SAND.2023.2,
  author =	{Shibata, Masahiro and Kitamura, Naoki and Eguchi, Ryota and Sudo, Yuichi and Nakamura, Junya and Kim, Yonghwan},
  title =	{{Partial Gathering of Mobile Agents in Dynamic Tori}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{2:1--2:22},
  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.2023.2},
  URN =		{urn:nbn:de:0030-drops-179387},
  doi =		{10.4230/LIPIcs.SAND.2023.2},
  annote =	{Keywords: distributed system, mobile agents, partial gathering, dynamic tori}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.33
New Clocks, Optimal Line Formation and Self-Replication Population Protocols

Authors: Leszek Gąsieniec, Paul G. Spirakis, and Grzegorz Stachowiak

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

Abstract
In this paper we consider a known variant of the standard population protocol model in which agents are allowed to be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ(n²) interactions in expectation which coincides with Θ(n) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O(polylog n) parallel time. The main focus of this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model. - We propose and analyze a novel edge based phase clock counting parallel time Θ(nlog n) in the network constructor model, showing also that its leader based counterpart provides the same time guarantees in the standard population protocol model. Note that all currently known phase clocks can count parallel time not exceeding O(polylog n). - We prove that any spanning line formation protocol requires Ω(nlog n) parallel time if high probability guaranty is imposed. We also show that the new clock enables an optimal O(nlog n) parallel time spanning line construction, which improves dramatically on the best currently known O(n²) parallel time protocol, solving the main open problem in the considered model [O. Michail and P. Spirakis, 2016]. - We propose a new probabilistic bubble-sort algorithm in which random comparisons and transfers are limited to the adjacent positions in the sequence. Utilising a novel potential function reasoning we show that rather surprisingly this probabilistic sorting procedure requires O(n²) comparisons in expectation and whp, and is on par with its deterministic counterpart. - We propose the first population protocol allowing self-replication of a strand of an arbitrary length k (carrying k-bit message of size independent of the state space) in parallel time O(n(k+log n)). The bit pipelining mechanism and the time complexity analysis of self-replication process mimic those used in the probabilistic bubble-sort argument. The new protocol permits also simultaneous self-replication, where l copies of the strand can be created in parallel in time O(n(k+log n)log l). We also discuss application of the strand self-replication protocol to pattern matching. All protocols are always correct and provide time guarantees with high probability defined as 1-n^(-η), for a constant η > 0.
Cite as

Leszek Gąsieniec, Paul G. Spirakis, and Grzegorz Stachowiak. New Clocks, Optimal Line Formation and Self-Replication Population Protocols. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gasieniec_et_al:LIPIcs.STACS.2023.33,
  author =	{G\k{a}sieniec, Leszek and Spirakis, Paul G. and Stachowiak, Grzegorz},
  title =	{{New Clocks, Optimal Line Formation and Self-Replication Population Protocols}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{33:1--33:22},
  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.2023.33},
  URN =		{urn:nbn:de:0030-drops-176857},
  doi =		{10.4230/LIPIcs.STACS.2023.33},
  annote =	{Keywords: Population protocols, constructors, probabilistic bubble-sort, self-replication}
}
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.
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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)

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@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
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.44
Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols

Authors: Leszek Gąsieniec, Paul Spirakis, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
In this paper we consider a known variant of the standard population protocol model in which agents can be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. The state space of agents is fixed (constant size) and the size n of the population is not known, i.e., not hard-coded in the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ(n²) interactions in expectation which coincides with Θ(n) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O(polylog n) parallel time. The main focus in this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model. - We propose and analyse a novel edge based phase clock counting parallel time Θ(nlog n) in the network constructor model, showing also that its leader based counterpart provides the same time guaranties in the standard population protocol model. Note that all currently known phase clocks can count parallel time not exceeding O(polylog n). - The new clock enables a nearly optimal O(nlog n) parallel time spanning line construction (a key component of universal network construction), which improves dramatically on the best currently known O(n²) parallel time protocol, solving the main open problem in the considered model [O. Michail and P. Spirakis, 2016]. - We propose a new probabilistic bubble-sort algorithm in which random comparisons and transfers are allowed only between the adjacent positions in the sequence. Utilising a novel potential function reasoning we show that rather surprisingly this probabilistic sorting (via conditional pipelining) procedure requires O(n²) comparisons in expectation and whp, and is on par with its deterministic counterpart. - We propose the first population protocol allowing self-replication of a strand of an arbitrary length k (carrying a k-bit message of size independent of the state space) in parallel time O(n(k+log n)). The pipelining mechanism and the time complexity analysis of the strand self-replication protocol mimic those used in the probabilistic bubble-sort. The new protocol permits also simultaneous self-replication, where l copies of the strand can be created in time O(n(k+log n)log l). Finally, we discuss application of the strand self-replication protocol to pattern matching. Our protocols are always correct and provide time guaranties with high probability defined as 1-n^{-η}, for a constant η > 0.
Cite as

Leszek Gąsieniec, Paul Spirakis, and Grzegorz Stachowiak. Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 44:1-44:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gasieniec_et_al:LIPIcs.DISC.2022.44,
  author =	{G\k{a}sieniec, Leszek and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{44:1--44:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.44},
  URN =		{urn:nbn:de:0030-drops-172351},
  doi =		{10.4230/LIPIcs.DISC.2022.44},
  annote =	{Keywords: Population protocols, network constructors, probabilistic bubble-sort, self-replication}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.62
The Complexity of Computing Optimum Labelings for Temporal Connectivity

Authors: Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis

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

Abstract
A graph is temporally connected if there exists a strict temporal path, i.e., a path whose edges have strictly increasing labels, from every vertex u to every other vertex v. In this paper we study temporal design problems for undirected temporally connected graphs. The basic setting of these optimization problems is as follows: given a connected undirected graph G, what is the smallest number |λ| of time-labels that we need to add to the edges of G such that the resulting temporal graph (G,λ) is temporally connected? As it turns out, this basic problem, called Minimum Labeling (ML), can be optimally solved in polynomial time. However, exploiting the temporal dimension, the problem becomes more interesting and meaningful in its following variations, which we investigate in this paper. First we consider the problem Min. Aged Labeling (MAL) of temporally connecting the graph when we are given an upper-bound on the allowed age (i.e., maximum label) of the obtained temporal graph (G,λ). Second we consider the problem Min. Steiner Labeling (MSL), where the aim is now to have a temporal path between any pair of "important" vertices which lie in a subset R ⊆ V, which we call the terminals. This relaxed problem resembles the problem Steiner Tree in static (i.e., non-temporal) graphs. However, due to the requirement of strictly increasing labels in a temporal path, Steiner Tree is not a special case of MSL. Finally we consider the age-restricted version of MSL, namely Min. Aged Steiner Labeling (MASL). Our main results are threefold: we prove that (i) MAL becomes NP-complete on undirected graphs, while (ii) MASL becomes W[1]-hard with respect to the number |R| of terminals. On the other hand we prove that (iii) although the age-unrestricted problem MSL remains NP-hard, it is in FPT with respect to the number |R| of terminals. That is, adding the age restriction, makes the above problems strictly harder (unless P=NP or W[1]=FPT).
Cite as

Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis. The Complexity of Computing Optimum Labelings for Temporal Connectivity. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 62:1-62:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{klobas_et_al:LIPIcs.MFCS.2022.62,
  author =	{Klobas, Nina and Mertzios, George B. and Molter, Hendrik and Spirakis, Paul G.},
  title =	{{The Complexity of Computing Optimum Labelings for Temporal Connectivity}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{62:1--62:15},
  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.2022.62},
  URN =		{urn:nbn:de:0030-drops-168603},
  doi =		{10.4230/LIPIcs.MFCS.2022.62},
  annote =	{Keywords: Temporal graph, graph labeling, foremost temporal path, temporal connectivity, Steiner Tree}
}
Document
DOI: 10.4230/LIPIcs.DNA.28.1
Fast and Robust Strand Displacement Cascades via Systematic Design Strategies

Authors: Tiernan Kennedy, Cadence Pearce, and Chris Thachuk

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
A barrier to wider adoption of molecular computation is the difficulty of implementing arbitrary chemical reaction networks (CRNs) that are robust and replicate the kinetics of designed behavior. DNA Strand Displacement (DSD) cascades have been a favored technology for this purpose due to their potential to emulate arbitrary CRNs and known principles to tune their reaction rates. Progress on leakless cascades has demonstrated that DSDs can be arbitrarily robust to spurious "leak" reactions when incorporating systematic domain level redundancy. These improvements in robustness result in slower kinetics of designed reactions. Existing work has demonstrated the kinetic and thermodynamic effects of sequence mismatch introduction and elimination during displacement. We present a systematic, sequence modification strategy for optimizing the kinetics of leakless cascades without practical cost to their robustness. An in-depth case study explores the effects of this optimization when applied to a typical leakless translator cascade. Thermodynamic analysis of energy barriers and kinetic experimental data support that DSD cascades can be fast and robust.
Cite as

Tiernan Kennedy, Cadence Pearce, and Chris Thachuk. Fast and Robust Strand Displacement Cascades via Systematic Design Strategies. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kennedy_et_al:LIPIcs.DNA.28.1,
  author =	{Kennedy, Tiernan and Pearce, Cadence and Thachuk, Chris},
  title =	{{Fast and Robust Strand Displacement Cascades via Systematic Design Strategies}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.1},
  URN =		{urn:nbn:de:0030-drops-167869},
  doi =		{10.4230/LIPIcs.DNA.28.1},
  annote =	{Keywords: DNA strand displacement, Energy barriers, Kinetics}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SAND.2022.2
Algorithmic Problems on Temporal Graphs (Invited Talk)

Authors: Paul G. Spirakis

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

Abstract
Research on Temporal Graphs has expanded in the last few years. Most of the results till now, address problems related to the notion of Temporal Paths (and Temporal Connectivity). In this talk, we focus, instead, on problems whose main topic is not on Temporal Paths. In particular, we will discuss Temporal Vertex Covers, the notion of Temporal Transitivity, and also issues and models of stochastic temporal graphs. We believe that several algorithmic graph problems, not directly related to paths, can be raised in the temporal domain. This may motivate new research towards lifting more topics of algorithmic graph theory to the temporal case.
Cite as

Paul G. Spirakis. Algorithmic Problems on Temporal Graphs (Invited Talk). In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{spirakis:LIPIcs.SAND.2022.2,
  author =	{Spirakis, Paul G.},
  title =	{{Algorithmic Problems on Temporal Graphs}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{2:1--2:1},
  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.2022.2},
  URN =		{urn:nbn:de:0030-drops-159446},
  doi =		{10.4230/LIPIcs.SAND.2022.2},
  annote =	{Keywords: Temporal graph, stochastic temporal graph, vertex cover, temporal transitivity}
}
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)

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@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
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.4
Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk)

Authors: Huijia (Rachel) Lin

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Indistinguishability obfuscation, introduced by Barak et al. [Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from the subexponential hardness of three well-founded assumptions. We prove the following. Theorem (Informal) Assume sub-exponential hardness for the following: - the Learning Parity with Noise (LPN) assumption over general prime fields 𝔽_p with polynomially many LPN samples and error rate 1/k^δ, where k is the dimension of the LPN secret, and δ > 0 is any constant; - the existence of a Boolean Pseudo-Random Generator (PRG) in NC⁰ with stretch n^(1+τ), where n is the length of the PRG seed, and τ > 0 is any constant; - the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exist. As a corollary, all cryptographic goals that can be achieved using indistinguishability obfuscation can now be achieved assuming the above three assumptions. This includes fully homomorphic encryption, functional encryption, multiparty non-interactive key-exchange, succinct garbled random access machine, and many others. This is joint work with Aayush Jain (UCLA and NTT Research) and Amit Sahai (UCLA).
Cite as

Huijia (Rachel) Lin. Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lin:LIPIcs.FSTTCS.2021.4,
  author =	{Lin, Huijia (Rachel)},
  title =	{{Indistinguishability Obfuscation from Well-Founded Assumptions}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.4},
  URN =		{urn:nbn:de:0030-drops-155154},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.4},
  annote =	{Keywords: Cryptography, indistinguishability obfuscation}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2021.19
Coderelictions for Free Exponential Modalities

Authors: Jean-Simon Pacaud Lemay

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
In a categorical model of the multiplicative and exponential fragments of intuitionistic linear logic (MELL), the exponential modality is interpreted as a comonad ! such that each cofree !-coalgebra !A comes equipped with a natural cocommutative comonoid structure. An important case is when ! is a free exponential modality so that !A is the cofree cocommutative comonoid over A. A categorical model of MELL with a free exponential modality is called a Lafont category. A categorical model of differential linear logic is called a differential category, where the differential structure can equivalently be described by a deriving transformation !A⊗A →{𝖽_A} !A or a codereliction A →{η_A} !A. Blute, Lucyshyn-Wright, and O'Neill showed that every Lafont category with finite biproducts is a differential category. However, from a differential linear logic perspective, Blute, Lucyshyn-Wright, and O'Neill’s approach is not the usual one since the result was stated in the dual setting and the proof is in terms of the deriving transformation 𝖽. In differential linear logic, it is often the codereliction η that is preferred and that plays a more prominent role. In this paper, we provide an alternative proof that every Lafont category (with finite biproducts) is a differential category, where we construct the codereliction η using the couniversal property of the cofree cocommtuative comonoid !A and show that η is unique. To achieve this, we introduce the notion of an infinitesimal augmentation k⊕A →{𝖧_A} !(k ⊕ A), which in particular is a !-coalgebra and a comonoid morphism, and show that infinitesimal augmentations are in bijective correspondence to coderelictions (and deriving transformations). As such, infinitesimal augmentations provide a new equivalent axiomatization for differential categories in terms of more commonly known concepts. For a free exponential modality, its infinitesimal augmentation is easy to construct and allows one to clearly see the differential structure of a Lafont category, regardless of the construction of !A.
Cite as

Jean-Simon Pacaud Lemay. Coderelictions for Free Exponential Modalities. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lemay:LIPIcs.CALCO.2021.19,
  author =	{Lemay, Jean-Simon Pacaud},
  title =	{{Coderelictions for Free Exponential Modalities}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio 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.CALCO.2021.19},
  URN =		{urn:nbn:de:0030-drops-153742},
  doi =		{10.4230/LIPIcs.CALCO.2021.19},
  annote =	{Keywords: Differential Categories, Coderelictions, Differential Linear Logic, Free Exponential Modalities, Lafont Categories, Infinitesimal Augmentations}
}
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