139 Search Results for "Spirakis, Paul"

Volume

LIPIcs, Volume 257

2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

SAND 2023, June 19-21, 2023, Pisa, Italy

Editors: David Doty and Paul Spirakis

Volume

LIPIcs, Volume 117

43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

MFCS 2018, August 27-31, 2018, Liverpool, GB

Editors: Igor Potapov, Paul Spirakis, and James Worrell

Document
DOI: 10.4230/LIPIcs.AofA.2024.22
The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension

Authors: Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
It is celebrated that a simple random walk on ℤ and ℤ² returns to the initial vertex v infinitely many times during infinitely many transitions, which is said recurrent, while it returns to v only finite times on ℤ^d for d ≥ 3, which is said transient. It is also known that a simple random walk on a growing region on ℤ^d can be recurrent depending on growing speed for any fixed d. This paper shows that a simple random walk on {0,1,…,N}ⁿ with an increasing n and a fixed N can be recurrent depending on the increasing speed of n. Precisely, we are concerned with a specific model of a random walk on a growing graph (RWoGG) and show a phase transition between the recurrence and transience of the random walk regarding the growth speed of the graph. For the proof, we develop a pausing coupling argument introducing the notion of weakly less homesick as graph growing (weakly LHaGG).
Cite as

Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai. The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kumamoto_et_al:LIPIcs.AofA.2024.22,
  author =	{Kumamoto, Shuma and Kijima, Shuji and Shirai, Tomoyuki},
  title =	{{The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.22},
  URN =		{urn:nbn:de:0030-drops-204577},
  doi =		{10.4230/LIPIcs.AofA.2024.22},
  annote =	{Keywords: Random walk, dynamic graph, recurrence, transience, coupling}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.16
NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials

Authors: Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha

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

Abstract
An s-sparse polynomial has at most s monomials with nonzero coefficients. The Equivalence Testing problem for sparse polynomials (ETsparse) asks to decide if a given polynomial f is equivalent to (i.e., in the orbit of) some s-sparse polynomial. In other words, given f ∈ 𝔽[𝐱] and s ∈ ℕ, ETsparse asks to check if there exist A ∈ GL(|𝐱|, 𝔽) and 𝐛 ∈ 𝔽^|𝐱| such that f(A𝐱 + 𝐛) is s-sparse. We show that ETsparse is NP-hard over any field 𝔽, if f is given in the sparse representation, i.e., as a list of nonzero coefficients and exponent vectors. This answers a question posed by Gupta, Saha and Thankey (SODA 2023) and also, more explicitly, by Baraskar, Dewan and Saha (STACS 2024). The result implies that the Minimum Circuit Size Problem (MCSP) is NP-hard for a dense subclass of depth-3 arithmetic circuits if the input is given in sparse representation. We also show that approximating the smallest s₀ such that a given s-sparse polynomial f is in the orbit of some s₀-sparse polynomial to within a factor of s^{1/3 - ε} is NP-hard for any ε > 0; observe that s-factor approximation is trivial as the input is s-sparse. Finally, we show that for any constant σ ≥ 6, checking if a polynomial (given in sparse representation) is in the orbit of some support-σ polynomial is NP-hard. Support of a polynomial f is the maximum number of variables present in any monomial of f. These results are obtained via direct reductions from the 3-SAT problem.
Cite as

Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha. NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baraskar_et_al:LIPIcs.ICALP.2024.16,
  author =	{Baraskar, Omkar and Dewan, Agrim and Saha, Chandan and Sinha, Pulkit},
  title =	{{NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.16},
  URN =		{urn:nbn:de:0030-drops-201598},
  doi =		{10.4230/LIPIcs.ICALP.2024.16},
  annote =	{Keywords: Equivalence testing, MCSP, sparse polynomials, 3SAT}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.55
Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous

Authors: Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.

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

Abstract
Temporal graphs are dynamic graphs where the edge set can change in each time step, while the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been widely studied. In this paper, we extend the concept of graph automorphisms from static graphs to temporal graphs and show for the first time that symmetries enable faster exploration: We prove that a connected temporal graph with n vertices and orbit number r (i.e., r is the number of automorphism orbits) can be explored in O(r n^{1+ε}) time steps, for any fixed ε > 0. For r = O(n^c) for constant c < 1, this is a significant improvement over the known tight worst-case bound of Θ(n²) time steps for arbitrary connected temporal graphs. We also give two lower bounds for temporal exploration, showing that Ω(n log n) time steps are required for some inputs with r = O(1) and that Ω(rn) time steps are required for some inputs for any r with 1 ≤ r ≤ n. Moreover, we show that the techniques we develop for fast exploration can be used to derive the following result for rendezvous: Two agents with different programs and without communication ability are placed by an adversary at arbitrary vertices and given full information about the connected temporal graph, except that they do not have consistent vertex labels. Then the two agents can meet at a common vertex after O(n^{1+ε}) time steps, for any constant ε > 0. For some connected temporal graphs with the orbit number being a constant, we also present a complementary lower bound of Ω(nlog n) time steps.
Cite as

Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.. Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dogeas_et_al:LIPIcs.ICALP.2024.55,
  author =	{Dogeas, Konstantinos and Erlebach, Thomas and Kammer, Frank and Meintrup, Johannes and Moses Jr., William K.},
  title =	{{Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{55:1--55:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.55},
  URN =		{urn:nbn:de:0030-drops-201989},
  doi =		{10.4230/LIPIcs.ICALP.2024.55},
  annote =	{Keywords: dynamic graphs, parameterized algorithms, algorithmic graph theory, graph automorphism, orbit number}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.26
Another Hamiltonian Cycle in Bipartite Pfaffian Graphs

Authors: Andreas Björklund, Petteri Kaski, and Jesper Nederlof

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

Abstract
Finding a Hamiltonian cycle in a given graph is computationally challenging, and in general remains so even when one is further given one Hamiltonian cycle in the graph and asked to find another. In fact, no significantly faster algorithms are known for finding another Hamiltonian cycle than for finding a first one even in the setting where another Hamiltonian cycle is structurally guaranteed to exist, such as for odd-degree graphs. We identify a graph class - the bipartite Pfaffian graphs of minimum degree three - where it is NP-complete to decide whether a given graph in the class is Hamiltonian, but when presented with a Hamiltonian cycle as part of the input, another Hamiltonian cycle can be found efficiently. We prove that Thomason’s lollipop method [Ann. Discrete Math., 1978], a well-known algorithm for finding another Hamiltonian cycle, runs in a linear number of steps in cubic bipartite Pfaffian graphs. This was conjectured for cubic bipartite planar graphs by Haddadan [MSc thesis, Waterloo, 2015]; in contrast, examples are known of both cubic bipartite graphs and cubic planar graphs where the lollipop method takes exponential time. Beyond the reach of the lollipop method, we address a slightly more general graph class and present two algorithms, one running in linear-time and one operating in logarithmic space, that take as input (i) a bipartite Pfaffian graph G of minimum degree three, (ii) a Hamiltonian cycle H in G, and (iii) an edge e in H, and output at least three other Hamiltonian cycles through the edge e in G. We also present further improved algorithms for finding optimal traveling salesperson tours and counting Hamiltonian cycles in bipartite planar graphs with running times that are not achieved yet in general planar graphs. Our technique also has purely graph-theoretical consequences; for example, we show that every cubic bipartite Pfaffian graph has either zero or at least six distinct Hamiltonian cycles; the latter case is tight for the cube graph.
Cite as

Andreas Björklund, Petteri Kaski, and Jesper Nederlof. Another Hamiltonian Cycle in Bipartite Pfaffian Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bjorklund_et_al:LIPIcs.ICALP.2024.26,
  author =	{Bj\"{o}rklund, Andreas and Kaski, Petteri and Nederlof, Jesper},
  title =	{{Another Hamiltonian Cycle in Bipartite Pfaffian Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{26:1--26:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.26},
  URN =		{urn:nbn:de:0030-drops-201692},
  doi =		{10.4230/LIPIcs.ICALP.2024.26},
  annote =	{Keywords: Another Hamiltonian cycle, Pfaffian graph, planar graph, Thomason’s lollipop method}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.84
The k-Opt Algorithm for the Traveling Salesman Problem Has Exponential Running Time for k ≥ 5

Authors: Sophia Heimann, Hung P. Hoang, and Stefan Hougardy

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

Abstract
The k-Opt algorithm is a local search algorithm for the Traveling Salesman Problem. Starting with an initial tour, it iteratively replaces at most k edges in the tour with the same number of edges to obtain a better tour. Krentel (FOCS 1989) showed that the Traveling Salesman Problem with the k-Opt neighborhood is complete for the class PLS (polynomial time local search) and that the k-Opt algorithm can have exponential running time for any pivot rule. However, his proof requires k ≫ 1000 and has a substantial gap. We show the two properties above for a much smaller value of k, addressing an open question by Monien, Dumrauf, and Tscheuschner (ICALP 2010). In particular, we prove the PLS-completeness for k ≥ 17 and the exponential running time for k ≥ 5.
Cite as

Sophia Heimann, Hung P. Hoang, and Stefan Hougardy. The k-Opt Algorithm for the Traveling Salesman Problem Has Exponential Running Time for k ≥ 5. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 84:1-84:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{heimann_et_al:LIPIcs.ICALP.2024.84,
  author =	{Heimann, Sophia and Hoang, Hung P. and Hougardy, Stefan},
  title =	{{The k-Opt Algorithm for the Traveling Salesman Problem Has Exponential Running Time for k ≥ 5}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{84:1--84:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.84},
  URN =		{urn:nbn:de:0030-drops-202270},
  doi =		{10.4230/LIPIcs.ICALP.2024.84},
  annote =	{Keywords: Traveling Salesman Problem, k-Opt algorithm, PLS-completeness}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.131
The Structure of Trees in the Pushdown Hierarchy

Authors: Arnaud Carayol and Lucien Charamond

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

Abstract
In this article, we investigate the structure of the trees in the pushdown hierarchy, a hierarchy of infinite graphs having a decidable MSO-theory. We show that a binary complete tree in the pushdown hierarchy must contain at least two different subtrees which are isomorphic. We extend this property to any tree with no leaves and with chains of unary vertices of bounded length. We provided two applications of this result. A first application in formal language theory, gives a simple argument to show that some languages are not deterministic higher-order indexed languages. A second application in number theory shows that the real numbers defined by deterministic higher-order pushdown automata are either rational or transcendental.
Cite as

Arnaud Carayol and Lucien Charamond. The Structure of Trees in the Pushdown Hierarchy. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 131:1-131:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{carayol_et_al:LIPIcs.ICALP.2024.131,
  author =	{Carayol, Arnaud and Charamond, Lucien},
  title =	{{The Structure of Trees in the Pushdown Hierarchy}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{131:1--131:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.131},
  URN =		{urn:nbn:de:0030-drops-202749},
  doi =		{10.4230/LIPIcs.ICALP.2024.131},
  annote =	{Keywords: Pushdown hierarchy, Monadic second-order logic, Automatic numbers}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.135
A Finite Presentation of Graphs of Treewidth at Most Three

Authors: Amina Doumane, Samuel Humeau, and Damien Pous

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

Abstract
We provide a finite equational presentation of graphs of treewidth at most three, solving an instance of an open problem by Courcelle and Engelfriet. We use a syntax generalising series-parallel expressions, denoting graphs with a small interface. We introduce appropriate notions of connectivity for such graphs (components, cutvertices, separation pairs). We use those concepts to analyse the structure of graphs of treewidth at most three, showing how they can be decomposed recursively, first canonically into connected parallel components, and then non-deterministically. The main difficulty consists in showing that all non-deterministic choices can be related using only finitely many equational axioms.
Cite as

Amina Doumane, Samuel Humeau, and Damien Pous. A Finite Presentation of Graphs of Treewidth at Most Three. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 135:1-135:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doumane_et_al:LIPIcs.ICALP.2024.135,
  author =	{Doumane, Amina and Humeau, Samuel and Pous, Damien},
  title =	{{A Finite Presentation of Graphs of Treewidth at Most Three}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{135:1--135:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.135},
  URN =		{urn:nbn:de:0030-drops-202787},
  doi =		{10.4230/LIPIcs.ICALP.2024.135},
  annote =	{Keywords: Graphs, treewidth, connectedness, axiomatisation, series-parallel expressions}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.136
Improved Algorithm for Reachability in d-VASS

Authors: Yuxi Fu, Qizhe Yang, and Yangluo Zheng

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

Abstract
An 𝖥_{d} upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where 𝖥_d is the d-th level of the Grzegorczyk hierarchy of complexity classes. The new algorithm combines the idea of the linear path scheme characterization of the reachability in the 2-dimension VASSes with the general decomposition algorithm by Mayr, Kosaraju and Lambert. The result improves the 𝖥_{d + 4} upper bound due to Leroux and Schmitz (LICS 2019).
Cite as

Yuxi Fu, Qizhe Yang, and Yangluo Zheng. Improved Algorithm for Reachability in d-VASS. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 136:1-136:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2024.136,
  author =	{Fu, Yuxi and Yang, Qizhe and Zheng, Yangluo},
  title =	{{Improved Algorithm for Reachability in d-VASS}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{136:1--136:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.136},
  URN =		{urn:nbn:de:0030-drops-202799},
  doi =		{10.4230/LIPIcs.ICALP.2024.136},
  annote =	{Keywords: Petri net, vector addition system, reachability}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.149
A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions

Authors: Wojciech Różowski

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

Abstract
Deterministic automata have been traditionally studied through the point of view of language equivalence, but another perspective is given by the canonical notion of shortest-distinguishing-word distance quantifying the of states. Intuitively, the longer the word needed to observe a difference between two states, then the closer their behaviour is. In this paper, we give a sound and complete axiomatisation of shortest-distinguishing-word distance between regular languages. Our axiomatisation relies on a recently developed quantitative analogue of equational logic, allowing to manipulate rational-indexed judgements of the form e ≡_ε f meaning term e is approximately equivalent to term f within the error margin of ε. The technical core of the paper is dedicated to the completeness argument that draws techniques from order theory and Banach spaces to simplify the calculation of the behavioural distance to the point it can be then mimicked by axiomatic reasoning.
Cite as

Wojciech Różowski. A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 149:1-149:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{rozowski:LIPIcs.ICALP.2024.149,
  author =	{R\'{o}\.{z}owski, Wojciech},
  title =	{{A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{149:1--149:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.149},
  URN =		{urn:nbn:de:0030-drops-202920},
  doi =		{10.4230/LIPIcs.ICALP.2024.149},
  annote =	{Keywords: Regular Expressions, Behavioural Distances, Quantitative Equational Theories}
}
Document
DOI: 10.4230/LIPIcs.SAND.2024.16
Temporal Graph Realization from Fastest Paths

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

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an n × n matrix D and a Δ ∈ ℕ, the goal is to construct a Δ-periodic temporal graph with n vertices such that the duration of a fastest path from v_i to v_j is equal to D_{i,j}, or to decide that such a temporal graph does not exist. The variations of the problem on static graphs has been well studied and understood since the 1960’s (e.g. [Erdős and Gallai, 1960], [Hakimi and Yau, 1965]). As it turns out, the periodic temporal graph realization problem has a very different computational complexity behavior than its static (i. e., non-temporal) counterpart. First we show that the problem is NP-hard in general, but polynomial-time solvable if the so-called underlying graph is a tree. Building upon those results, we investigate its parameterized computational complexity with respect to structural parameters of the underlying static graph which measure the "tree-likeness". We prove a tight classification between such parameters that allow fixed-parameter tractability (FPT) and those which imply W[1]-hardness. We show that our problem is W[1]-hard when parameterized by the feedback vertex number (and therefore also any smaller parameter such as treewidth, degeneracy, and cliquewidth) of the underlying graph, while we show that it is in FPT when parameterized by the feedback edge number (and therefore also any larger parameter such as maximum leaf number) of the underlying graph.
Cite as

Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis. Temporal Graph Realization from Fastest Paths. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{klobas_et_al:LIPIcs.SAND.2024.16,
  author =	{Klobas, Nina and Mertzios, George B. and Molter, Hendrik and Spirakis, Paul G.},
  title =	{{Temporal Graph Realization from Fastest Paths}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.16},
  URN =		{urn:nbn:de:0030-drops-198945},
  doi =		{10.4230/LIPIcs.SAND.2024.16},
  annote =	{Keywords: Temporal graph, periodic temporal labeling, fastest temporal path, graph realization, temporal connectivity, parameterized complexity}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2024.22
Brief Announcement: Collision-Free Robot Scheduling

Authors: Duncan Adamson, Nathan Flaherty, Igor Potapov, and Paul G. Spirakis

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
Robots are becoming an increasingly common part of scientific work within laboratory environments. In this paper, we investigate the problem of designing schedules for completing a set of tasks at fixed locations with multiple robots in a laboratory. We represent the laboratory as a graph with tasks placed on fixed vertices and robots represented as agents, with the constraint that no two robots may occupy the same vertex, or traverse the same edge, at the same time. Each schedule is partitioned into a set of timesteps, corresponding to a walk through the graph (allowing for a robot to wait at a vertex to complete a task), with each timestep taking time equal to the time for a robot to move from one vertex to another and each task taking some given number of timesteps during the completion of which a robot must stay at the vertex containing the task. The goal is to determine a set of schedules, with one schedule for each robot, minimising the number of timesteps taken by the schedule taking the greatest number of timesteps within the set of schedules. We show that the problem of finding a task-fulfilling schedule in at most L timesteps is NP-complete for many simple classes of graphs. Explicitly, we provide this result for complete graphs, bipartite graphs, star graphs, and planar graphs. Finally, we provide positive results for line graphs, showing that we can find an optimal set of schedules for k robots completing m tasks of equal length of a path of length n in O(kmn) time, and a k-approximation when the length of the tasks is unbounded.
Cite as

Duncan Adamson, Nathan Flaherty, Igor Potapov, and Paul G. Spirakis. Brief Announcement: Collision-Free Robot Scheduling. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 22:1-22:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{adamson_et_al:LIPIcs.SAND.2024.22,
  author =	{Adamson, Duncan and Flaherty, Nathan and Potapov, Igor and Spirakis, Paul G.},
  title =	{{Brief Announcement: Collision-Free Robot Scheduling}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{22:1--22:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.22},
  URN =		{urn:nbn:de:0030-drops-199004},
  doi =		{10.4230/LIPIcs.SAND.2024.22},
  annote =	{Keywords: Graph Exploration, Scheduling, NP-Completeness, Approximation Algorithms}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2024.27
Brief Announcement: On the Existence of δ-Temporal Cliques in Random Simple Temporal Graphs

Authors: George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos, and Paul G. Spirakis

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
We consider random simple temporal graphs in which every edge of the complete graph K_n appears once within the time interval [0,1] independently and uniformly at random. Our main result is a sharp threshold on the size of any maximum δ-clique (namely a clique with edges appearing at most δ apart within [0,1]) in random instances of this model, for any constant δ. In particular, using the probabilistic method, we prove that the size of a maximum δ-clique is approximately (2 log n)/(log 1/δ) with high probability (whp). What seems surprising is that, even though the random simple temporal graph contains Θ(n²) overlapping δ-windows, which (when viewed separately) correspond to different random instances of the Erdős-Rényi random graphs model, the size of the maximum δ-clique in the former model and the maximum clique size of the latter are approximately the same. Furthermore, we show that the minimum interval containing a δ-clique is δ-o(δ) whp. We use this result to show that any polynomial time algorithm for δ-Temporal Clique is unlikely to have very large probability of success.
Cite as

George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos, and Paul G. Spirakis. Brief Announcement: On the Existence of δ-Temporal Cliques in Random Simple Temporal Graphs. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 27:1-27:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mertzios_et_al:LIPIcs.SAND.2024.27,
  author =	{Mertzios, George B. and Nikoletseas, Sotiris and Raptopoulos, Christoforos and Spirakis, Paul G.},
  title =	{{Brief Announcement: On the Existence of \delta-Temporal Cliques in Random Simple Temporal Graphs}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{27:1--27:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.27},
  URN =		{urn:nbn:de:0030-drops-199056},
  doi =		{10.4230/LIPIcs.SAND.2024.27},
  annote =	{Keywords: Simple random temporal graph, \delta-temporal clique, probabilistic method}
}
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.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}
}
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