Volume
LIPIcs, Volume 306
49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS)
Event
MFCS 2024, August 26-30, 2024, Bratislava, SlovakiaEditors
- Comenius University, Faculty of Mathematics, Physics, and Informatics, Bratislava, Slovakia
Publication Details
- published at: 2024-08-23
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-335-5
- DBLP: db/conf/mfcs/mfcs2024
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Complete Volume
LIPIcs, Volume 306, MFCS 2024, Complete Volume
Abstract
LIPIcs, Volume 306, MFCS 2024, Complete Volume
Cite as
49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 1-1362, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@Proceedings{kralovic_et_al:LIPIcs.MFCS.2024,
title = {{LIPIcs, Volume 306, MFCS 2024, Complete Volume}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {1--1362},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024},
URN = {urn:nbn:de:0030-drops-205555},
doi = {10.4230/LIPIcs.MFCS.2024},
annote = {Keywords: LIPIcs, Volume 306, MFCS 2024, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{kralovic_et_al:LIPIcs.MFCS.2024.0,
author = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {0:i--0:xviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.0},
URN = {urn:nbn:de:0030-drops-205568},
doi = {10.4230/LIPIcs.MFCS.2024.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Paper
On Key Parameters Affecting the Realizability of Degree Sequences (Invited Paper)
Abstract
Call a sequence d = (d_1,d_2, …, d_n) of positive integers graphic, planaric, outer-planaric, or forestic if it is the degree sequence of some arbitrary, planar, outer-planar, or cycle-free graph G, respectively. The two extreme classes of graphic and forestic sequences were given full characterizations. (The latter has a particularly simple criterion: d is forestic if and only if its volume, ∑ d ≡ ∑_i d_i, satisfies ∑ d ≤ 2n - 2.) In contrast, the problems of fully characterizing planaric and outer-planaric degree sequences are still open.
In this paper, we discuss the parameters affecting the realizability of degree sequences by restricted classes of sparse graph, including planar graphs, outerplanar graphs, and some of their subclasses (e.g., 2-trees and cactus graphs). A key parameter is the volume of the sequence d, namely, ∑ d which is twice the number of edges in the realizing graph. For planar graphs, for example, an obvious consequence of Euler’s theorem is that an n-element sequence d satisfying ∑ d > 4n-6 cannot be planaric. Hence, ∑ d ≤ 4n-6 is a necessary condition for d to be planaric. What about the opposite direction? Is there an upper bound on ∑ d that guarantees that if d is graphic then it is also planaric. Does the answer depend on additional parameters? The same questions apply also to sub-classes of the planar graphs.
A concrete example that is illustrated in the technical part of the paper is the class of outer-planaric degree sequences. Denoting the number of 1’s in d by ω₁, we show that for a graphic sequence d, if ω₁ = 0 then d is outer-planaric when ∑ d ≤ 3n-3, and if ω₁ > 0 then d is outer-planaric when ∑ d ≤ 3n-ω₁-2. Conversely, we show that there are graphic sequences that are not outer-planaric with ω₁ = 0 and ∑ d = 3n-2, as well as ones with ω₁ > 0 and ∑ d = 3n-ω₁-1.
Cite as
Amotz Bar-Noy, Toni Böhnlein, David Peleg, Yingli Ran, and Dror Rawitz. On Key Parameters Affecting the Realizability of Degree Sequences (Invited Paper). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{barnoy_et_al:LIPIcs.MFCS.2024.1,
author = {Bar-Noy, Amotz and B\"{o}hnlein, Toni and Peleg, David and Ran, Yingli and Rawitz, Dror},
title = {{On Key Parameters Affecting the Realizability of Degree Sequences}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {1:1--1:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.1},
URN = {urn:nbn:de:0030-drops-205573},
doi = {10.4230/LIPIcs.MFCS.2024.1},
annote = {Keywords: Degree Sequences, Graph Algorithms, Graph Realization, Outer-planar Graphs}
}
Document
Invited Paper
Challenges of the Reachability Problem in Infinite-State Systems (Invited Paper)
Abstract
The reachability problem is a central problem for various infinite state systems like automata with pushdown, with different kinds of counters or combinations thereof. Despite its centrality and decades of research the community still lacks a lot of answers for fundamental and basic questions of that type. I briefly describe my personal viewpoint on the current state of art and emphasise interesting directions, which are worth investigating in my opinion. I also formulate several easy to formulate and understand challenges, which might be pretty hard to solve but at the same time illustrate fundamental lack of our understanding in the area.
Cite as
Wojciech Czerwiński. Challenges of the Reachability Problem in Infinite-State Systems (Invited Paper). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 2:1-2:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{czerwinski:LIPIcs.MFCS.2024.2,
author = {Czerwi\'{n}ski, Wojciech},
title = {{Challenges of the Reachability Problem in Infinite-State Systems}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {2:1--2:8},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.2},
URN = {urn:nbn:de:0030-drops-205582},
doi = {10.4230/LIPIcs.MFCS.2024.2},
annote = {Keywords: reachability problem, infinite-state systems, vector addition systems, pushdown}
}
Document
Invited Talk
On Low Complexity Colorings of Grids (Invited Talk)
Abstract
A d-dimensional configuration is a coloring of the infinite grid ℤ^d using a finite number of colors. For a finite subset D ⊆ ℤ^d, the D-patterns of a configuration are the patterns of shape D that appear in the configuration. A configuration is said to be admitted by these patterns. The number of distinct D-patterns in a configuration is a natural measure of its complexity. We focus on low complexity configurations, where the number of distinct D-patterns is at most |D|, the size of the shape. This framework includes the notorious open Nivat’s conjecture and the recently solved Periodic Tiling problem. We use algebraic tools to study the periodicity of low complexity configurations. In the two-dimensional case, if D ⊆ ℤ² is a rectangle or any convex shape, we establish an algorithm to determine if a given collection of |D| patterns admits any configuration. This is based on the fact that if the given patterns admit a configuration, then they admit a periodic configuration. We also demonstrate that a two-dimensional low complexity configuration must be periodic if it originates from the well-known Ledrappier subshift or from several other algebraically defined subshifts.
Cite as
Jarkko Kari. On Low Complexity Colorings of Grids (Invited Talk). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{kari:LIPIcs.MFCS.2024.3,
author = {Kari, Jarkko},
title = {{On Low Complexity Colorings of Grids}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {3:1--3:2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.3},
URN = {urn:nbn:de:0030-drops-205590},
doi = {10.4230/LIPIcs.MFCS.2024.3},
annote = {Keywords: symbolic dynamics, Nivat’s conjecture, Periodic tiling problem, periodicity, low pattern complexity, annihilator}
}
Document
Invited Paper
From TCS to Learning Theory (Invited Paper)
Abstract
While machine learning theory and theoretical computer science are both based on a solid mathematical foundation, the two research communities have a smaller overlap than what the proximity of the fields warrant. In this invited abstract, I will argue that traditional theoretical computer scientists have much to offer the learning theory community and vice versa. I will make this argument by telling a personal story of how I broadened my research focus to encompass learning theory, and how my TCS background has been extremely useful in doing so. It is my hope that this personal account may inspire more TCS researchers to tackle the many elegant and important theoretical questions that learning theory has to offer.
Cite as
Kasper Green Larsen. From TCS to Learning Theory (Invited Paper). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 4:1-4:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{larsen:LIPIcs.MFCS.2024.4,
author = {Larsen, Kasper Green},
title = {{From TCS to Learning Theory}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {4:1--4:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.4},
URN = {urn:nbn:de:0030-drops-205603},
doi = {10.4230/LIPIcs.MFCS.2024.4},
annote = {Keywords: Theoretical Computer Science, Learning Theory}
}
Document
Invited Talk
Fine-Grained Complexity of Program Analysis (Invited Talk)
Abstract
There is a well-known "cubic bottleneck" in program analysis and language theory: many program analysis problems can be solved in time cubic in the size of the input but, despite years of effort, there are no known sub-cubic algorithms. For example, context-free reachability (whether there is a path in a labeled graph that is labeled with a word from a context-free language), the emptiness problem for pushdown automata, and the recognition problem for two-way nondeterministic pushdown automata all belong to the cubic class. We survey the status of these problems through the lens of fine-grained complexity.
We study the related certification task: given an instance of any of these problems, are there small and efficiently checkable certificates for the existence and for the non-existence of a path? We show that, in both scenarios, there exist succinct certificates (O(n²) in the size of the problem) and these certificates can be checked in subcubic (matrix multiplication) time. Thus, all these problems lie in nondeterministic and co-nondeterministic subcubic time.
We also study a hierarchy of program analysis problems above the cubic bottleneck. A representative problem here is the recognition problem for two-way nondeterministic pushdown automata with k heads. We show fine-grained hardness results for this hierarchy.
We also discuss purely language-theoretic consequences of these results: for example, we obtain hardest languages accepted by two-way nondeterministic multihead pushdown automata, as well as separations between language classes.
(Joint work with A. R. Balasubramanian, Dmitry Chistikov, and Philipp Schepper.)
Cite as
Rupak Majumdar. Fine-Grained Complexity of Program Analysis (Invited Talk). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, p. 5:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{majumdar:LIPIcs.MFCS.2024.5,
author = {Majumdar, Rupak},
title = {{Fine-Grained Complexity of Program Analysis}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {5:1--5:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.5},
URN = {urn:nbn:de:0030-drops-205619},
doi = {10.4230/LIPIcs.MFCS.2024.5},
annote = {Keywords: Fine-grained complexity, CFL reachability, 2NPDA recognition, PDA emptiness}
}
Document
Monotonicity of the Cops and Robber Game for Bounded Depth Treewidth
Abstract
We study a variation of the cops and robber game characterising treewidth, where in each round at most one cop may be placed and in each play at most q rounds are played, where q is a parameter of the game. We prove that if k cops have a winning strategy in this game, then k cops have a monotone winning strategy. As a corollary we obtain a new characterisation of bounded depth treewidth, and we give a positive answer to an open question by Fluck, Seppelt and Spitzer (2024), thus showing that graph classes of bounded depth treewidth are homomorphism distinguishing closed.
Our proof of monotonicity substantially reorganises a winning strategy by first transforming it into a pre-tree decomposition, which is inspired by decompositions of matroids, and then applying an intricate breadth-first "cleaning up" procedure along the pre-tree decomposition (which may temporarily lose the property of representing a strategy), in order to achieve monotonicity while controlling the number of rounds simultaneously across all branches of the decomposition via a vertex exchange argument. We believe this can be useful in future research.
Cite as
Isolde Adler and Eva Fluck. Monotonicity of the Cops and Robber Game for Bounded Depth Treewidth. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{adler_et_al:LIPIcs.MFCS.2024.6,
author = {Adler, Isolde and Fluck, Eva},
title = {{Monotonicity of the Cops and Robber Game for Bounded Depth Treewidth}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {6:1--6:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.6},
URN = {urn:nbn:de:0030-drops-205621},
doi = {10.4230/LIPIcs.MFCS.2024.6},
annote = {Keywords: tree decompositions, treewidth, treedepth, cops-and-robber game, monotonicity, homomorphism distinguishing closure}
}
Document
Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower Bounds
Abstract
The Polynomial-Time Hierarchy (PH) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to "quantum advantage" analyses for near-term quantum computers. Quantumly, however, despite the fact that at least four definitions of quantum PH exist, it has been challenging to prove analogues for these of even basic facts from PH. This work studies three quantum-verifier based generalizations of PH, two of which are from [Gharibian, Santha, Sikora, Sundaram, Yirka, 2022] and use classical strings (QCPH) and quantum mixed states (QPH) as proofs, and one of which is new to this work, utilizing quantum pure states (QPHpure) as proofs. We first resolve several open problems from [GSSSY22], including a collapse theorem and a Karp-Lipton theorem for QCPH. Then, for our new class QPHpure, we show one-sided error reduction QPHpure, as well as the first bounds relating these quantum variants of PH, namely QCPH ⊆ QPHpure ⊆ EXP^PP.
Cite as
Avantika Agarwal, Sevag Gharibian, Venkata Koppula, and Dorian Rudolph. Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower Bounds. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{agarwal_et_al:LIPIcs.MFCS.2024.7,
author = {Agarwal, Avantika and Gharibian, Sevag and Koppula, Venkata and Rudolph, Dorian},
title = {{Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower Bounds}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {7:1--7:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.7},
URN = {urn:nbn:de:0030-drops-205632},
doi = {10.4230/LIPIcs.MFCS.2024.7},
annote = {Keywords: Quantum complexity, polynomial hierarchy}
}
Document
Sublinear Time Shortest Path in Expander Graphs
Abstract
Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case. However, several works have shown how to solve this problem in sublinear time in expectation when the input graph is drawn from one of several classes of random graphs. In this work, we extend these results by giving sublinear time shortest path (and short path) algorithms for expander graphs. We thus identify a natural deterministic property of a graph (that is satisfied by typical random regular graphs) which suffices for sublinear time shortest paths. The algorithms are very simple, involving only bidirectional breadth first search and short random walks. We also complement our new algorithms by near-matching lower bounds.
Cite as
Noga Alon, Allan Grønlund, Søren Fuglede Jørgensen, and Kasper Green Larsen. Sublinear Time Shortest Path in Expander Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{alon_et_al:LIPIcs.MFCS.2024.8,
author = {Alon, Noga and Gr{\o}nlund, Allan and J{\o}rgensen, S{\o}ren Fuglede and Larsen, Kasper Green},
title = {{Sublinear Time Shortest Path in Expander Graphs}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {8:1--8:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.8},
URN = {urn:nbn:de:0030-drops-205646},
doi = {10.4230/LIPIcs.MFCS.2024.8},
annote = {Keywords: Shortest Path, Expanders, Breadth First Search, Graph Algorithms}
}
Document
Quantum Algorithms for Hopcroft’s Problem
Abstract
In this work we study quantum algorithms for Hopcroft’s problem which is a fundamental problem in computational geometry. Given n points and n lines in the plane, the task is to determine whether there is a point-line incidence. The classical complexity of this problem is well-studied, with the best known algorithm running in O(n^{4/3}) time, with matching lower bounds in some restricted settings. Our results are two different quantum algorithms with time complexity Õ(n^{5/6}). The first algorithm is based on partition trees and the quantum backtracking algorithm. The second algorithm uses a quantum walk together with a history-independent dynamic data structure for storing line arrangement which supports efficient point location queries. In the setting where the number of points and lines differ, the quantum walk-based algorithm is asymptotically faster. The quantum speedups for the aforementioned data structures may be useful for other geometric problems.
Cite as
Vladimirs Andrejevs, Aleksandrs Belovs, and Jevgēnijs Vihrovs. Quantum Algorithms for Hopcroft’s Problem. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{andrejevs_et_al:LIPIcs.MFCS.2024.9,
author = {Andrejevs, Vladimirs and Belovs, Aleksandrs and Vihrovs, Jevg\={e}nijs},
title = {{Quantum Algorithms for Hopcroft’s Problem}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {9:1--9:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.9},
URN = {urn:nbn:de:0030-drops-205653},
doi = {10.4230/LIPIcs.MFCS.2024.9},
annote = {Keywords: Quantum algorithms, Quantum walks, Computational Geometry}
}
Document
A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations
Abstract
Implicit computational complexity is an active area of theoretical computer science, which aims at providing machine-independent characterizations of relevant complexity classes. One of the seminal works in this field appeared in 1965, when Cobham introduced a function algebra closed under bounded recursion on notation to capture FP. Later on, several complexity classes have been characterized using limited recursion schemas. In this context, a new approach was recently introduced, showing that ordinary differential equations (ODEs) offer a natural tool for algorithmic design and providing a characterization of FP by an ODE-schema. The overall goal of the present work is precisely that of generalizing this approach to parallel computation, obtaining an original ODE-characterization for the small circuit classes FAC⁰ and FTC⁰.
Cite as
Melissa Antonelli, Arnaud Durand, and Juha Kontinen. A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{antonelli_et_al:LIPIcs.MFCS.2024.10,
author = {Antonelli, Melissa and Durand, Arnaud and Kontinen, Juha},
title = {{A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {10:1--10:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.10},
URN = {urn:nbn:de:0030-drops-205664},
doi = {10.4230/LIPIcs.MFCS.2024.10},
annote = {Keywords: Implicit computational complexity, parallel computation, ordinary differential equations, circuit complexity}
}
Document
Switching Classes: Characterization and Computation
Abstract
In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class 𝒢, we are concerned with the maximum subclass and the minimum superclass of 𝒢 that are closed under switching. We characterize the maximum subclass for many important classes 𝒢, and prove that it is finite when 𝒢 is minor-closed and omits at least one graph. For several graph classes, we develop polynomial-time algorithms to recognize the minimum superclass. We also show that the recognition of the superclass is NP-hard for H-free graphs when H is a sufficiently long path or cycle, and it cannot be solved in subexponential time assuming the Exponential Time Hypothesis.
Cite as
Dhanyamol Antony, Yixin Cao, Sagartanu Pal, and R. B. Sandeep. Switching Classes: Characterization and Computation. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{antony_et_al:LIPIcs.MFCS.2024.11,
author = {Antony, Dhanyamol and Cao, Yixin and Pal, Sagartanu and Sandeep, R. B.},
title = {{Switching Classes: Characterization and Computation}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {11:1--11:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.11},
URN = {urn:nbn:de:0030-drops-205678},
doi = {10.4230/LIPIcs.MFCS.2024.11},
annote = {Keywords: Switching, Graph modification, Minor-closed graph class, Hereditary graph class}
}
Document
Generalizing Roberts' Characterization of Unit Interval Graphs
Abstract
For any natural number d, a graph G is a (disjoint) d-interval graph if it is the intersection graph of (disjoint) d-intervals, the union of d (disjoint) intervals on the real line. Two important subclasses of d-interval graphs are unit and balanced d-interval graphs (where every interval has unit length or all the intervals associated to a same vertex have the same length, respectively). A celebrated result by Roberts gives a simple characterization of unit interval graphs being exactly claw-free interval graphs. Here, we study the generalization of this characterization for d-interval graphs. In particular, we prove that for any d ⩾ 2, if G is a K_{1,2d+1}-free interval graph, then G is a unit d-interval graph. However, somehow surprisingly, under the same assumptions, G is not always a disjoint unit d-interval graph. This implies that the class of disjoint unit d-interval graphs is strictly included in the class of unit d-interval graphs. Finally, we study the relationships between the classes obtained under disjoint and non-disjoint d-intervals in the balanced case and show that the classes of disjoint balanced 2-intervals and balanced 2-intervals coincide, but this is no longer true for d > 2.
Cite as
Virginia Ardévol Martínez, Romeo Rizzi, Abdallah Saffidine, Florian Sikora, and Stéphane Vialette. Generalizing Roberts' Characterization of Unit Interval Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{ardevolmartinez_et_al:LIPIcs.MFCS.2024.12,
author = {Ard\'{e}vol Mart{\'\i}nez, Virginia and Rizzi, Romeo and Saffidine, Abdallah and Sikora, Florian and Vialette, St\'{e}phane},
title = {{Generalizing Roberts' Characterization of Unit Interval Graphs}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {12:1--12:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.12},
URN = {urn:nbn:de:0030-drops-205687},
doi = {10.4230/LIPIcs.MFCS.2024.12},
annote = {Keywords: Interval graphs, Multiple Interval Graphs, Unit Interval Graphs, Characterization}
}
Document
A Direct Translation from LTL with Past to Deterministic Rabin Automata
Abstract
We present a translation from linear temporal logic with past to deterministic Rabin automata. The translation is direct in the sense that it does not rely on intermediate non-deterministic automata, and asymptotically optimal, resulting in Rabin automata of doubly exponential size. It is based on two main notions. One is that it is possible to encode the history contained in the prefix of a word, as relevant for the formula under consideration, by performing simple rewrites of the formula itself. As a consequence, a formula involving past operators can (through such rewrites, which involve alternating between weak and strong versions of past operators in the formula’s syntax tree) be correctly evaluated at an arbitrary point in the future without requiring backtracking through the word. The other is that this allows us to generalize to linear temporal logic with past the result that the language of a pure-future formula can be decomposed into a Boolean combination of simpler languages, for which deterministic automata with simple acceptance conditions are easily constructed.
Cite as
Shaun Azzopardi, David Lidell, and Nir Piterman. A Direct Translation from LTL with Past to Deterministic Rabin Automata. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{azzopardi_et_al:LIPIcs.MFCS.2024.13,
author = {Azzopardi, Shaun and Lidell, David and Piterman, Nir},
title = {{A Direct Translation from LTL with Past to Deterministic Rabin Automata}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {13:1--13:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.13},
URN = {urn:nbn:de:0030-drops-205694},
doi = {10.4230/LIPIcs.MFCS.2024.13},
annote = {Keywords: Linear temporal logic, \omega-automata, determinization}
}
Document
Logical Characterizations of Weighted Complexity Classes
Abstract
Fagin’s seminal result characterizing NP in terms of existential second-order logic started the fruitful field of descriptive complexity theory. In recent years, there has been much interest in the investigation of quantitative (weighted) models of computations. In this paper, we start the study of descriptive complexity based on weighted Turing machines over arbitrary semirings. We provide machine-independent characterizations (over ordered structures) of the weighted complexity classes NP[𝒮], FP[𝒮], FPLOG[𝒮], FPSPACE[𝒮], and FPSPACE_poly[𝒮] in terms of definability in suitable weighted logics for an arbitrary semiring 𝒮. In particular, we prove weighted versions of Fagin’s theorem (even for arbitrary structures, not necessarily ordered, provided that the semiring is idempotent and commutative), the Immerman-Vardi’s theorem (originally for 𝖯) and the Abiteboul-Vianu-Vardi’s theorem (originally for PSPACE). We also discuss a recent open problem proposed by Eiter and Kiesel.
Recently, the above mentioned weighted complexity classes have been investigated in connection to classical counting complexity classes. Furthermore, several classical counting complexity classes have been characterized in terms of particular weighted logics over the semiring ℕ of natural numbers. In this work, we cover several of these classes and obtain new results for others such as NPMV, ⊕𝖯, or the collection of real-valued languages realized by polynomial-time real-valued nondeterministic Turing machines. Furthermore, our results apply to classes based on many other important semirings, such as the max-plus and the min-plus semirings over the natural numbers which correspond to the classical classes MaxP[O(log n)] and MinP[O(log n)], respectively.
Cite as
Guillermo Badia, Manfred Droste, Carles Noguera, and Erik Paul. Logical Characterizations of Weighted Complexity Classes. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{badia_et_al:LIPIcs.MFCS.2024.14,
author = {Badia, Guillermo and Droste, Manfred and Noguera, Carles and Paul, Erik},
title = {{Logical Characterizations of Weighted Complexity Classes}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {14:1--14:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.14},
URN = {urn:nbn:de:0030-drops-205707},
doi = {10.4230/LIPIcs.MFCS.2024.14},
annote = {Keywords: Descriptive complexity, Weighted Turing machines, Weighted logics, Semirings}
}
Document
Breaking the Barrier 2^k for Subset Feedback Vertex Set in Chordal Graphs
Abstract
The Subset Feedback Vertex Set problem (SFVS) is to delete k vertices from a given graph such that in the remaining graph, any vertex in a subset T of vertices (called a terminal set) is not in a cycle. The famous Feedback Vertex Set problem is the special case of SFVS with T being the whole set of vertices. In this paper, we study exact algorithms for SFVS in Split Graphs (SFVS-S) and SFVS in Chordal Graphs (SFVS-C). SFVS-S generalizes the minimum vertex cover problem and the prize-collecting version of the maximum independent set problem in hypergraphs (PCMIS), and SFVS-C further generalizes SFVS-S. Both SFVS-S and SFVS-C are implicit 3-Hitting Set problems. However, it is not easy to solve them faster than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica 2019) proved that SFVS-C can be solved in 𝒪^*(2^k) time, slightly improving the best result 𝒪^*(2.0755^k) for 3-Hitting Set. In this paper, we break the "2^k-barrier" for SFVS-S and SFVS-C by introducing an 𝒪^*(1.8192^k)-time algorithm. This achievement also indicates that PCMIS can be solved in 𝒪^*(1.8192ⁿ) time, marking the first exact algorithm for PCMIS that outperforms the trivial 𝒪^*(2ⁿ) threshold. Our algorithm uses reduction and branching rules based on the Dulmage-Mendelsohn decomposition and a divide-and-conquer method.
Cite as
Tian Bai and Mingyu Xiao. Breaking the Barrier 2^k for Subset Feedback Vertex Set in Chordal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bai_et_al:LIPIcs.MFCS.2024.15,
author = {Bai, Tian and Xiao, Mingyu},
title = {{Breaking the Barrier 2^k for Subset Feedback Vertex Set in Chordal Graphs}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {15:1--15:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.15},
URN = {urn:nbn:de:0030-drops-205711},
doi = {10.4230/LIPIcs.MFCS.2024.15},
annote = {Keywords: Subset Feedback Vertex Set, Prize-Collecting Maximum Independent Set, Parameterized Algorithms, Split Graphs, Chordal Graphs, Dulmage-Mendelsohn Decomposition}
}
Document
Tractability of Packing Vertex-Disjoint A-Paths Under Length Constraints
Abstract
Given an undirected graph G and a set A ⊆ V(G), an A-path is a path in G that starts and ends at two distinct vertices of A with intermediate vertices in V(G)⧵A. An A-path is called an (A,𝓁)-path if the length of the path is exactly 𝓁. In the (A, 𝓁)-Path Packing problem (ALPP), we seek to determine whether there exist k vertex-disjoint (A, 𝓁)-paths in G or not.
The problem is already known to be fixed-parmeter tractable when parameterized by k+𝓁 via color coding while it remains Para-NP-hard when parameterized by k (Hamiltonian Path) or 𝓁 (P₃-Partition) alone. Therefore, a logical direction to pursue this problem is to examine it in relation to structural parameters. Belmonte et al. initiated a study along these lines and proved that ALPP parameterized by pw+|A| is W[1]-hard where pw is the pathwidth of G. In this paper, we strengthen their result and prove that it is unlikely that ALPP is fixed-parameter tractable even with respect to a bigger parameter (|A|+dtp) where dtp denotes the distance between G and a path graph (distance to path). We use a randomized reduction to achieve the mentioned result. Toward this, we prove a lemma similar to the influential "isolation lemma": Given a set system (X,ℱ) if the elements of X are assigned a weight uniformly at random from a set of values fairly large, then each subset in ℱ will have a unique weight with high probability. We believe that this result will be useful beyond the scope of this paper.
ALPP being hard even for structural parameters like distance to path+|A| rules out the possibility of any FPT algorithms for many well-known other structural parameters, including FVS+|A| and treewidth+|A|. There is a straightforward FPT algorithm for ALPP parameterized by vc, the vertex cover number of the input graph. Following this, we consider the parameters CVD(cluster vertex deletion)+|A| and CVD+|𝓁| and show the problem to be FPT with respect to these parameters. Note that CVD is incomparable to the treewidth of a graph and has been in vogue recently.
Cite as
Susobhan Bandopadhyay, Aritra Banik, Diptapriyo Majumdar, and Abhishek Sahu. Tractability of Packing Vertex-Disjoint A-Paths Under Length Constraints. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bandopadhyay_et_al:LIPIcs.MFCS.2024.16,
author = {Bandopadhyay, Susobhan and Banik, Aritra and Majumdar, Diptapriyo and Sahu, Abhishek},
title = {{Tractability of Packing Vertex-Disjoint A-Paths Under Length Constraints}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {16:1--16:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.16},
URN = {urn:nbn:de:0030-drops-205725},
doi = {10.4230/LIPIcs.MFCS.2024.16},
annote = {Keywords: Parameterized complexity, (A,𝓁)-Path Packing, Kernelization, Randomized-Exponential Time Hypothesis, Graph Classes}
}
Document
On the Descriptive Complexity of Vertex Deletion Problems
Abstract
Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property. Regarding k as the parameter, a dichotomy was recently shown based on the number of quantifier alternations of first-order formulas that describe the property. In this paper, we refine this classification by moving from quantifier alternations to individual quantifier patterns and from a dichotomy to a trichotomy, resulting in a complete classification of the complexity of vertex deletion problems based on their quantifier pattern. The more fine-grained approach uncovers new tractable fragments, which we show to not only lie in FPT, but even in parameterized constant-depth circuit complexity classes. On the other hand, we show that vertex deletion becomes intractable already for just one quantifier per alternation, that is, there is a formula of the form ∀ x∃ y∀ z (ψ), with ψ quantifier-free, for which the vertex deletion problem is W[1]-hard. The fine-grained analysis also allows us to uncover differences in the complexity landscape when we consider different kinds of graphs and more general structures: While basic graphs (undirected graphs without self-loops), undirected graphs, and directed graphs each have a different frontier of tractability, the frontier for arbitrary logical structures coincides with that of directed graphs.
Cite as
Max Bannach, Florian Chudigiewitsch, and Till Tantau. On the Descriptive Complexity of Vertex Deletion Problems. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bannach_et_al:LIPIcs.MFCS.2024.17,
author = {Bannach, Max and Chudigiewitsch, Florian and Tantau, Till},
title = {{On the Descriptive Complexity of Vertex Deletion Problems}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {17:1--17:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.17},
URN = {urn:nbn:de:0030-drops-205733},
doi = {10.4230/LIPIcs.MFCS.2024.17},
annote = {Keywords: graph problems, fixed-parameter tractability, descriptive complexity, vertex deletion}
}
Document
Sparse Graphic Degree Sequences Have Planar Realizations
Abstract
A sequence d = (d_1,d_2, …, d_n) of positive integers is graphic if it is the degree sequence of some simple graph G, and planaric if it is the degree sequence of some simple planar graph G. It is known that if ∑ d ≤ 2n - 2, then d has a realization by a forest, hence it is trivially planaric. In this paper, we seek bounds on ∑ d that guarantee that if d is graphic then it is also planaric. We show that this holds true when ∑ d ≤ 4n-4-2ω₁, where ω₁ is the number of 1’s in d. Conversely, we show that there are graphic sequences with ∑ d = 4n-2ω₁ that are non-planaric. For the case ω₁ = 0, we show that d is planaric when ∑ d ≤ 4n-4. Conversely, we show that there is a graphic sequence with ∑ d = 4n-2 that is non-planaric. In fact, when ∑ d ≤ 4n-6-2ω₁, d can be realized by a graph with a 2-page book embedding.
Cite as
Amotz Bar-Noy, Toni Böhnlein, David Peleg, Yingli Ran, and Dror Rawitz. Sparse Graphic Degree Sequences Have Planar Realizations. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{barnoy_et_al:LIPIcs.MFCS.2024.18,
author = {Bar-Noy, Amotz and B\"{o}hnlein, Toni and Peleg, David and Ran, Yingli and Rawitz, Dror},
title = {{Sparse Graphic Degree Sequences Have Planar Realizations}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {18:1--18:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.18},
URN = {urn:nbn:de:0030-drops-205745},
doi = {10.4230/LIPIcs.MFCS.2024.18},
annote = {Keywords: Degree Sequences, Graph Algorithms, Graph Realization, Planar Graphs}
}
Document
The Canadian Traveller Problem on Outerplanar Graphs
Abstract
We study the k-Canadian Traveller Problem, where a weighted graph G = (V,E,ω) with a source s ∈ V and a target t ∈ V are given. This problem also has a hidden input E_* ⊊ E of cardinality at most k representing blocked edges. The objective is to travel from s to t with the minimum distance. At the beginning of the walk, the blockages E_* are unknown: the traveller discovers that an edge is blocked when visiting one of its endpoints. Online algorithms, also called strategies, have been proposed for this problem and assessed with the competitive ratio, i.e., the ratio between the distance actually traversed by the traveller divided by the distance he would have traversed knowing the blockages in advance.
Even though the optimal competitive ratio is 2k+1 even on unit-weighted planar graphs of treewidth 2, we design a polynomial-time strategy achieving competitive ratio 9 on unit-weighted outerplanar graphs. This value 9 also stands as a lower bound for this family of graphs as we prove that, for any ε > 0, no strategy can achieve a competitive ratio 9-ε. Finally, we show that it is not possible to achieve a constant competitive ratio (independent of G and k) on weighted outerplanar graphs.
Cite as
Laurent Beaudou, Pierre Bergé, Vsevolod Chernyshev, Antoine Dailly, Yan Gerard, Aurélie Lagoutte, Vincent Limouzy, and Lucas Pastor. The Canadian Traveller Problem on Outerplanar Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{beaudou_et_al:LIPIcs.MFCS.2024.19,
author = {Beaudou, Laurent and Berg\'{e}, Pierre and Chernyshev, Vsevolod and Dailly, Antoine and Gerard, Yan and Lagoutte, Aur\'{e}lie and Limouzy, Vincent and Pastor, Lucas},
title = {{The Canadian Traveller Problem on Outerplanar Graphs}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {19:1--19:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.19},
URN = {urn:nbn:de:0030-drops-205750},
doi = {10.4230/LIPIcs.MFCS.2024.19},
annote = {Keywords: Canadian Traveller Problem, Online algorithms, Competitive analysis, Outerplanar graphs}
}
Document
Simple Qudit ZX and ZH Calculi, via Integrals
Abstract
The ZX calculus and ZH calculus use diagrams to denote and compute properties of quantum operations, using "rewrite rules" to transform between diagrams which denote the same operator through a functorial semantic map. Different semantic maps give rise to different rewrite systems, which may prove more convenient for different purposes. Using discrete measures, we describe semantic maps for ZX and ZH diagrams, well-suited to analyse unitary circuits and measurements on qudits of any fixed dimension D > 1 as a single "ZXH-calculus". We demonstrate rewrite rules for the "stabiliser fragment" of the ZX calculus and a "multicharacter fragment" of the ZH calculus.
Cite as
Niel de Beaudrap and Richard D. P. East. Simple Qudit ZX and ZH Calculi, via Integrals. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{debeaudrap_et_al:LIPIcs.MFCS.2024.20,
author = {de Beaudrap, Niel and East, Richard D. P.},
title = {{Simple Qudit ZX and ZH Calculi, via Integrals}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {20:1--20:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.20},
URN = {urn:nbn:de:0030-drops-205761},
doi = {10.4230/LIPIcs.MFCS.2024.20},
annote = {Keywords: ZX-calculus, ZH-calculus, qudits, string diagrams, discrete integrals}
}
Document
On Complexity of Confluence and Church-Rosser Proofs
Abstract
In this paper, we investigate confluence and the Church-Rosser property - two well-studied properties of rewriting and the λ-calculus - from the viewpoint of proof complexity. With respect to confluence, and focusing on orthogonal term rewrite systems, our main contribution is that the size, measured in number of symbols, of the smallest rewrite proof is polynomial in the size of the peak. For the Church-Rosser property we obtain exponential lower bounds for the size of the join in the size of the equality proof. Finally, we study the complexity of proving confluence in the context of the λ-calculus. Here, we establish an exponential (worst-case) lower bound of the size of the join in the size of the peak.
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Arnold Beckmann and Georg Moser. On Complexity of Confluence and Church-Rosser Proofs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{beckmann_et_al:LIPIcs.MFCS.2024.21,
author = {Beckmann, Arnold and Moser, Georg},
title = {{On Complexity of Confluence and Church-Rosser Proofs}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {21:1--21:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.21},
URN = {urn:nbn:de:0030-drops-205774},
doi = {10.4230/LIPIcs.MFCS.2024.21},
annote = {Keywords: logic, bounded arithmetic, consistency, rewriting}
}
Document
Graph Search Trees and the Intermezzo Problem
Abstract
The last in-tree recognition problem asks whether a given spanning tree can be derived by connecting each vertex with its rightmost left neighbor of some search ordering. In this study, we demonstrate that the last-in-tree recognition problem for Generic Search is NP-complete. We utilize this finding to strengthen a complexity result from order theory. Given a partial order π and a set of triples, the NP-complete intermezzo problem asks for a linear extension of π where each first element of a triple is not between the other two. We show that this problem remains NP-complete even when the Hasse diagram of the partial order forms a tree of bounded height. In contrast, we give an XP-algorithm for the problem when parameterized by the width of the partial order. Furthermore, we show that - under the assumption of the Exponential Time Hypothesis - the running time of this algorithm is asymptotically optimal.
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Jesse Beisegel, Ekkehard Köhler, Fabienne Ratajczak, Robert Scheffler, and Martin Strehler. Graph Search Trees and the Intermezzo Problem. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{beisegel_et_al:LIPIcs.MFCS.2024.22,
author = {Beisegel, Jesse and K\"{o}hler, Ekkehard and Ratajczak, Fabienne and Scheffler, Robert and Strehler, Martin},
title = {{Graph Search Trees and the Intermezzo Problem}},
booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
pages = {22:1--22:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-335-5},
ISSN = {1868-8969},
year = {2024},
volume = {306},
editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.22},
URN = {urn:nbn:de:0030-drops-205781},
doi = {10.4230/LIPIcs.MFCS.2024.22},
annote = {Keywords: graph search trees, intermezzo problem, algorithm, parameterized complexity}
}
Document
Minimizing Cost Register Automata over a Field
Abstract
Weighted automata (WA) are an extension of finite automata that define functions from words to values in a given semiring. An alternative deterministic model, called Cost Register Automata (CRA), was introduced by Alur et al. It enriches deterministic finite automata with a finite number of registers, which store values, updated at each transition using the operations of the semiring. It is known that CRA with register updates defined by linear maps have the same expressiveness as WA. Previous works have studied the register minimization problem: given a function computable by a WA and an integer k, is it possible to realize it using a CRA with at most k registers?
In this paper, we solve this problem for CRA over a field with linear register updates, using the notion of linear hull, an algebraic invariant of WA introduced recently by Bell and Smertnig. We then generalise the approach to solve a more challenging problem, that consists in minimizing simultaneously the number of states and that of registers. In addition, we also lift our results to the setting of CRA with affine updates. Last, while the linear hull was recently shown to be computable by Bell and Smertnig, no complexity bounds were given. To fill this gap, we provide two new algorithms to compute invariants of WA. This allows us to show that the register (resp. state-register) minimization problem can be solved in 2-ExpTime (resp. in NExpTime).
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Yahia Idriss Benalioua, Nathan Lhote, and Pierre-Alain Reynier. Minimizing Cost Register Automata over a Field. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leib