73 Search Results for "K�nigs, Alexander"

Document
DOI: 10.4230/LIPIcs.STACS.2024.4
Max Weight Independent Set in Sparse Graphs with No Long Claws

Authors: Tara Abrishami, Maria Chudnovsky, Marcin Pilipczuk, and Paweł Rzążewski

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

Abstract
We revisit the recent polynomial-time algorithm for the Max Weight Independent Set (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami, Chudnovsky, Dibek, Rzążewski, SODA 2022]. First, we show that with an arguably simpler approach we can obtain a faster algorithm with running time n^{𝒪(Δ²)}, where n is the number of vertices of the instance and Δ is the maximum degree. Then we combine our technique with known results concerning tree decompositions and provide a polynomial-time algorithm for MWIS in graphs excluding a fixed graph whose every component is a subdivided claw as an induced subgraph, and a fixed biclique as a subgraph.
Cite as

Tara Abrishami, Maria Chudnovsky, Marcin Pilipczuk, and Paweł Rzążewski. Max Weight Independent Set in Sparse Graphs with No Long Claws. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abrishami_et_al:LIPIcs.STACS.2024.4,
  author =	{Abrishami, Tara and Chudnovsky, Maria and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Max Weight Independent Set in Sparse Graphs with No Long Claws}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.4},
  URN =		{urn:nbn:de:0030-drops-197148},
  doi =		{10.4230/LIPIcs.STACS.2024.4},
  annote =	{Keywords: Max Weight Independent Set, subdivided claw, hereditary classes}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.10
Expressive Quantale-Valued Logics for Coalgebras: An Adjunction-Based Approach

Authors: Harsh Beohar, Sebastian Gurke, Barbara König, Karla Messing, Jonas Forster, Lutz Schröder, and Paul Wild

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

Abstract
We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on an earlier work that obtains Hennessy-Milner theorems as corollaries to a fixpoint preservation property along Galois connections between suitable lattices. We instantiate this to the setting of coalgebras, in which we spell out the compatibility property ensuring that we can derive a behaviour function whose greatest fixpoint coincides with the logical conformance. We then concentrate on the linear-time case, for which we study coalgebras based on the machine functor living in Eilenberg-Moore categories, a scenario for which we obtain a particularly simple logic and fixpoint equation. The theory is instantiated to concrete examples, both in the branching-time case (bisimilarity and behavioural metrics) and in the linear-time case (trace equivalences and trace distances).
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Harsh Beohar, Sebastian Gurke, Barbara König, Karla Messing, Jonas Forster, Lutz Schröder, and Paul Wild. Expressive Quantale-Valued Logics for Coalgebras: An Adjunction-Based Approach. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{beohar_et_al:LIPIcs.STACS.2024.10,
  author =	{Beohar, Harsh and Gurke, Sebastian and K\"{o}nig, Barbara and Messing, Karla and Forster, Jonas and Schr\"{o}der, Lutz and Wild, Paul},
  title =	{{Expressive Quantale-Valued Logics for Coalgebras: An Adjunction-Based Approach}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.10},
  URN =		{urn:nbn:de:0030-drops-197203},
  doi =		{10.4230/LIPIcs.STACS.2024.10},
  annote =	{Keywords: modal logics, coalgebras, behavioural equivalences, behavioural metrics, linear-time semantics, Eilenberg-Moore categories}
}
Document
DOI: 10.4230/OASIcs.NG-RES.2024.4
History-Based Run-Time Requirement Enforcement of Non-Functional Properties on MPSoCs

Authors: Khalil Esper and Jürgen Teich

Published in: OASIcs, Volume 117, Fifth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2024)

Abstract
Embedded system applications usually have requirements regarding non-functional properties of their execution like latency or power consumption. Enforcement of such requirements can be implemented by a reactive control loop, where an enforcer determines based on a system response (feedback) how to control the system, e.g., by selecting the number of active cores allocated to a program or by scaling their voltage/frequency mode. It is of a particular interest to design enforcement strategies for which it is possible to provide formal guarantees with respect to requirement violations, especially under a largely varying environmental input (workload) per execution. In this paper, we consider enforcement strategies that are modeled by a finite state machine (FSM) and the environment by a discrete-time Markov chain. Such a formalization enables the formal verification of temporal properties (verification goals) regarding the satisfaction of requirements of a given enforcement strategy. In this paper, we propose history-based enforcement FSMs which compute a reaction not just on the current, but on a fixed history of K previously observed system responses. We then analyze the quality of such enforcement FSMs in terms of the probability of satisfying a given set of verification goals and compare them to enforcement FSMs that react solely on the current system response. As experimental results, we present three use cases while considering requirements on latency and power consumption. The results show that history-based enforcement FSMs outperform enforcement FSMs that only consider the current system response regarding the probability of satisfying a given set of verification goals.
Cite as

Khalil Esper and Jürgen Teich. History-Based Run-Time Requirement Enforcement of Non-Functional Properties on MPSoCs. In Fifth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2024). Open Access Series in Informatics (OASIcs), Volume 117, pp. 4:1-4:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{esper_et_al:OASIcs.NG-RES.2024.4,
  author =	{Esper, Khalil and Teich, J\"{u}rgen},
  title =	{{History-Based Run-Time Requirement Enforcement of Non-Functional Properties on MPSoCs}},
  booktitle =	{Fifth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2024)},
  pages =	{4:1--4:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-313-3},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{117},
  editor =	{Yomsi, Patrick Meumeu and Wildermann, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.NG-RES.2024.4},
  URN =		{urn:nbn:de:0030-drops-197074},
  doi =		{10.4230/OASIcs.NG-RES.2024.4},
  annote =	{Keywords: Verification, Runtime Requirement Enforcement, History, Latency}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.24
Classical Verification of Quantum Learning

Authors: Matthias C. Caro, Marcel Hinsche, Marios Ioannou, Alexander Nietner, and Ryan Sweke

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required to facilitate widespread access to quantum learning advantages. Building on a recently introduced framework of interactive proof systems for classical machine learning, we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover. Concretely, we consider the problems of agnostic learning parities and Fourier-sparse functions with respect to distributions with uniform input marginal. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples, based on which we give efficient quantum learning algorithms for these tasks. Moreover, we prove that agnostic quantum parity and Fourier-sparse learning can be efficiently verified by a classical verifier with only random example or statistical query access. Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.
Cite as

Matthias C. Caro, Marcel Hinsche, Marios Ioannou, Alexander Nietner, and Ryan Sweke. Classical Verification of Quantum Learning. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 24:1-24:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{caro_et_al:LIPIcs.ITCS.2024.24,
  author =	{Caro, Matthias C. and Hinsche, Marcel and Ioannou, Marios and Nietner, Alexander and Sweke, Ryan},
  title =	{{Classical Verification of Quantum Learning}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{24:1--24:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.24},
  URN =		{urn:nbn:de:0030-drops-195524},
  doi =		{10.4230/LIPIcs.ITCS.2024.24},
  annote =	{Keywords: computational learning theory, quantum learning theory, interactive proofs, quantum oracles, agnostic learning}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.69
Quantum and Classical Low-Degree Learning via a Dimension-Free Remez Inequality

Authors: Ohad Klein, Joseph Slote, Alexander Volberg, and Haonan Zhang

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Recent efforts in Analysis of Boolean Functions aim to extend core results to new spaces, including to the slice binom([n],k), the hypergrid [K]ⁿ, and noncommutative spaces (matrix algebras). We present here a new way to relate functions on the hypergrid (or products of cyclic groups) to their harmonic extensions over the polytorus. We show the supremum of a function f over products of the cyclic group {exp(2π i k/K)}_{k = 1}^K controls the supremum of f over the entire polytorus ({z ∈ ℂ:|z| = 1}ⁿ), with multiplicative constant C depending on K and deg(f) only. This Remez-type inequality appears to be the first such estimate that is dimension-free (i.e., C does not depend on n). This dimension-free Remez-type inequality removes the main technical barrier to giving 𝒪(log n) sample complexity, polytime algorithms for learning low-degree polynomials on the hypergrid and low-degree observables on level-K qudit systems. In particular, our dimension-free Remez inequality implies new Bohnenblust-Hille-type estimates which are central to the learning algorithms and appear unobtainable via standard techniques. Thus we extend to new spaces a recent line of work [Eskenazis and Ivanisvili, 2022; Huang et al., 2022; Volberg and Zhang, 2023] that gave similarly efficient methods for learning low-degree polynomials on the hypercube and observables on qubits. An additional product of these efforts is a new class of distributions over which arbitrary quantum observables are well-approximated by their low-degree truncations - a phenomenon that greatly extends the reach of low-degree learning in quantum science [Huang et al., 2022].
Cite as

Ohad Klein, Joseph Slote, Alexander Volberg, and Haonan Zhang. Quantum and Classical Low-Degree Learning via a Dimension-Free Remez Inequality. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 69:1-69:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{klein_et_al:LIPIcs.ITCS.2024.69,
  author =	{Klein, Ohad and Slote, Joseph and Volberg, Alexander and Zhang, Haonan},
  title =	{{Quantum and Classical Low-Degree Learning via a Dimension-Free Remez Inequality}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{69:1--69:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.69},
  URN =		{urn:nbn:de:0030-drops-195977},
  doi =		{10.4230/LIPIcs.ITCS.2024.69},
  annote =	{Keywords: Analysis of Boolean Functions, Remez Inequality, Bohnenblust-Hille Inequality, Statistical Learning Theory, Qudits}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.36
Coloring and Recognizing Mixed Interval Graphs

Authors: Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
A mixed interval graph is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are defined by the geometry of intervals. In a proper coloring of a mixed interval graph G, an interval u receives a lower (different) color than an interval v if G contains arc (u,v) (edge {u,v}). Coloring of mixed graphs has applications, for example, in scheduling with precedence constraints; see a survey by Sotskov [Mathematics, 2020]. For coloring general mixed interval graphs, we present a min {ω(G), λ(G)+1}-approximation algorithm, where ω(G) is the size of a largest clique and λ(G) is the length of a longest directed path in G. For the subclass of bidirectional interval graphs (introduced recently for an application in graph drawing), we show that optimal coloring is NP-hard. This was known for general mixed interval graphs. We introduce a new natural class of mixed interval graphs, which we call containment interval graphs. In such a graph, there is an arc (u,v) if interval u contains interval v, and there is an edge {u,v} if u and v overlap. We show that these graphs can be recognized in polynomial time, that coloring them with the minimum number of colors is NP-hard, and that there is a 2-approximation algorithm for coloring.
Cite as

Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink. Coloring and Recognizing Mixed Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gutowski_et_al:LIPIcs.ISAAC.2023.36,
  author =	{Gutowski, Grzegorz and Junosza-Szaniawski, Konstanty and Klesen, Felix and Rz\k{a}\.{z}ewski, Pawe{\l} and Wolff, Alexander and Zink, Johannes},
  title =	{{Coloring and Recognizing Mixed Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.36},
  URN =		{urn:nbn:de:0030-drops-193388},
  doi =		{10.4230/LIPIcs.ISAAC.2023.36},
  annote =	{Keywords: Interval Graphs, Mixed Graphs, Graph Coloring}
}
Document
DOI: 10.4230/LIPIcs.TIME.2023.3
LSCPM: Communities in Massive Real-World Link Streams by Clique Percolation Method

Authors: Alexis Baudin, Lionel Tabourier, and Clémence Magnien

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

Abstract
Community detection is a popular approach to understand the organization of interactions in static networks. For that purpose, the Clique Percolation Method (CPM), which involves the percolation of k-cliques, is a well-studied technique that offers several advantages. Besides, studying interactions that occur over time is useful in various contexts, which can be modeled by the link stream formalism. The Dynamic Clique Percolation Method (DCPM) has been proposed for extending CPM to temporal networks. However, existing implementations are unable to handle massive datasets. We present a novel algorithm that adapts CPM to link streams, which has the advantage that it allows us to speed up the computation time with respect to the existing DCPM method. We evaluate it experimentally on real datasets and show that it scales to massive link streams. For example, it allows to obtain a complete set of communities in under twenty-five minutes for a dataset with thirty million links, what the state of the art fails to achieve even after a week of computation. We further show that our method provides communities similar to DCPM, but slightly more aggregated. We exhibit the relevance of the obtained communities in real world cases, and show that they provide information on the importance of vertices in the link streams.
Cite as

Alexis Baudin, Lionel Tabourier, and Clémence Magnien. LSCPM: Communities in Massive Real-World Link Streams by Clique Percolation Method. In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baudin_et_al:LIPIcs.TIME.2023.3,
  author =	{Baudin, Alexis and Tabourier, Lionel and Magnien, Cl\'{e}mence},
  title =	{{LSCPM: Communities in Massive Real-World Link Streams by Clique Percolation Method}},
  booktitle =	{30th International Symposium on Temporal Representation and Reasoning (TIME 2023)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-298-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{278},
  editor =	{Artikis, Alexander and Bruse, Florian and Hunsberger, Luke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.3},
  URN =		{urn:nbn:de:0030-drops-190932},
  doi =		{10.4230/LIPIcs.TIME.2023.3},
  annote =	{Keywords: Temporal network, Link stream, k-clique, Community detection, Clique Percolation Method, Real-world interactions}
}
Document
Extended Abstract
DOI: 10.4230/LIPIcs.TIME.2023.20
Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster (Extended Abstract)

Authors: Luke Hunsberger and Roberto Posenato

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

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

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

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@InProceedings{hunsberger_et_al:LIPIcs.TIME.2023.20,
  author =	{Hunsberger, Luke and Posenato, Roberto},
  title =	{{Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster}},
  booktitle =	{30th International Symposium on Temporal Representation and Reasoning (TIME 2023)},
  pages =	{20:1--20:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-298-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{278},
  editor =	{Artikis, Alexander and Bruse, Florian and Hunsberger, Luke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.20},
  URN =		{urn:nbn:de:0030-drops-191104},
  doi =		{10.4230/LIPIcs.TIME.2023.20},
  annote =	{Keywords: Temporal constraint networks, contingent durations, dispatchable network}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.65
Range Avoidance for Constant Depth Circuits: Hardness and Algorithms

Authors: Karthik Gajulapalli, Alexander Golovnev, Satyajeet Nagargoje, and Sidhant Saraogi

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
Range Avoidance (Avoid) is a total search problem where, given a Boolean circuit 𝖢: {0,1}ⁿ → {0,1}^m, m > n, the task is to find a y ∈ {0,1}^m outside the range of 𝖢. For an integer k ≥ 2, NC⁰_k-Avoid is a special case of Avoid where each output bit of 𝖢 depends on at most k input bits. While there is a very natural randomized algorithm for Avoid, a deterministic algorithm for the problem would have many interesting consequences. Ren, Santhanam, and Wang (FOCS 2022) and Guruswami, Lyu, and Wang (RANDOM 2022) proved that explicit constructions of functions of high formula complexity, rigid matrices, and optimal linear codes, reduce to NC⁰₄-Avoid, thus establishing conditional hardness of the NC⁰₄-Avoid problem. On the other hand, NC⁰₂-Avoid admits polynomial-time algorithms, leaving the question about the complexity of NC⁰₃-Avoid open. We give the first reduction of an explicit construction question to NC⁰₃-Avoid. Specifically, we prove that a polynomial-time algorithm (with an NP oracle) for NC⁰₃-Avoid for the case of m = n+n^{2/3} would imply an explicit construction of a rigid matrix, and, thus, a super-linear lower bound on the size of log-depth circuits. We also give deterministic polynomial-time algorithms for all NC⁰_k-Avoid problems for m ≥ n^{k-1}/log(n). Prior work required an NP oracle, and required larger stretch, m ≥ n^{k-1}.
Cite as

Karthik Gajulapalli, Alexander Golovnev, Satyajeet Nagargoje, and Sidhant Saraogi. Range Avoidance for Constant Depth Circuits: Hardness and Algorithms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 65:1-65:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gajulapalli_et_al:LIPIcs.APPROX/RANDOM.2023.65,
  author =	{Gajulapalli, Karthik and Golovnev, Alexander and Nagargoje, Satyajeet and Saraogi, Sidhant},
  title =	{{Range Avoidance for Constant Depth Circuits: Hardness and Algorithms}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{65:1--65:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.65},
  URN =		{urn:nbn:de:0030-drops-188901},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.65},
  annote =	{Keywords: Boolean function analysis, Explicit Constructions, Low-depth Circuits, Range Avoidance, Matrix Rigidity, Circuit Lower Bounds}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.20
Sparse Higher Order Čech Filtrations

Authors: Mickaël Buchet, Bianca B. Dornelas, and Michael Kerber

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

Abstract
For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the construction is the union-of-balls filtration that is popular in topological data analysis. For larger k, it yields a cleaner shape reconstruction in the presence of outliers. We contribute a sparsification algorithm to approximate the topology of the k-fold filtration. Our method is a combination and adaptation of several techniques from the well-studied case k = 1, resulting in a sparsification of linear size that can be computed in expected near-linear time with respect to the number of input points.
Cite as

Mickaël Buchet, Bianca B. Dornelas, and Michael Kerber. Sparse Higher Order Čech Filtrations. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{buchet_et_al:LIPIcs.SoCG.2023.20,
  author =	{Buchet, Micka\"{e}l and B. Dornelas, Bianca and Kerber, Michael},
  title =	{{Sparse Higher Order \v{C}ech Filtrations}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20},
  URN =		{urn:nbn:de:0030-drops-178709},
  doi =		{10.4230/LIPIcs.SoCG.2023.20},
  annote =	{Keywords: Sparsification, k-fold cover, Higher order \v{C}ech complexes}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.43
Constant-Depth Sorting Networks

Authors: Natalia Dobrokhotova-Maikova, Alexander Kozachinskiy, and Vladimir Podolskii

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
In this paper, we address sorting networks that are constructed from comparators of arity k > 2. I.e., in our setting the arity of the comparators - or, in other words, the number of inputs that can be sorted at the unit cost - is a parameter. We study its relationship with two other parameters - n, the number of inputs, and d, the depth. This model received considerable attention. Partly, its motivation is to better understand the structure of sorting networks. In particular, sorting networks with large arity are related to recursive constructions of ordinary sorting networks. Additionally, studies of this model have natural correspondence with a recent line of work on constructing circuits for majority functions from majority gates of lower fan-in. Motivated by these questions, we initiate the studies of lower bounds for constant-depth sorting networks. More precisely, we consider sorting networks of constant depth d and estimate the minimal k for which there is such a network with comparators of arity k. We prove tight lower bounds for d ≤ 4. More precisely, for depths d = 1,2 we observe that k = n. For d = 3 we show that k = ⌈n/2⌉. As our main result, we show that for d = 4 the minimal arity becomes sublinear: k = Θ(n^{2/3}). This contrasts with the case of majority circuits, in which k = O(n^{2/3}) is achievable already for depth d = 3. To prove these results, we develop a new combinatorial technique based on the notion of access to cells of a sorting network.
Cite as

Natalia Dobrokhotova-Maikova, Alexander Kozachinskiy, and Vladimir Podolskii. Constant-Depth Sorting Networks. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dobrokhotovamaikova_et_al:LIPIcs.ITCS.2023.43,
  author =	{Dobrokhotova-Maikova, Natalia and Kozachinskiy, Alexander and Podolskii, Vladimir},
  title =	{{Constant-Depth Sorting Networks}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{43:1--43:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.43},
  URN =		{urn:nbn:de:0030-drops-175468},
  doi =		{10.4230/LIPIcs.ITCS.2023.43},
  annote =	{Keywords: Sorting networks, constant depth, lower bounds, threshold circuits}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.39
On Finding Short Reconfiguration Sequences Between Independent Sets

Authors: Akanksha Agrawal, Soumita Hait, and Amer E. Mouawad

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Assume we are given a graph G, two independent sets S and T in G of size k ≥ 1, and a positive integer 𝓁 ≥ 1. The goal is to decide whether there exists a sequence ⟨ I₀, I₁, ..., I_𝓁 ⟩ of independent sets such that for all j ∈ {0,…,𝓁-1} the set I_j is an independent set of size k, I₀ = S, I_𝓁 = T, and I_{j+1} is obtained from I_j by a predetermined reconfiguration rule. We consider two reconfiguration rules, namely token sliding and token jumping. Intuitively, we view each independent set as a collection of tokens placed on the vertices of the graph. Then, the Token Sliding Optimization (TSO) problem asks whether there exists a sequence of at most 𝓁 steps that transforms S into T, where at each step we are allowed to slide one token from a vertex to an unoccupied neighboring vertex (while maintaining independence). In the Token Jumping Optimization (TJO) problem, at each step, we are allowed to jump one token from a vertex to any other unoccupied vertex of the graph (as long as we maintain independence). Both TSO and TJO are known to be fixed-parameter tractable when parameterized by 𝓁 on nowhere dense classes of graphs. In this work, we investigate the boundary of tractability for sparse classes of graphs. We show that both problems are fixed-parameter tractable for parameter k + 𝓁 + d on d-degenerate graphs as well as for parameter |M| + 𝓁 + Δ on graphs having a modulator M whose deletion leaves a graph of maximum degree Δ. We complement these result by showing that for parameter 𝓁 alone both problems become W[1]-hard already on 2-degenerate graphs. Our positive result makes use of the notion of independence covering families introduced by Lokshtanov et al. [Daniel Lokshtanov et al., 2020]. Finally, we show as a side result that using such families we can obtain a simpler and unified algorithm for the standard Token Jumping Reachability problem (a.k.a. Token Jumping) parameterized by k on both degenerate and nowhere dense classes of graphs.
Cite as

Akanksha Agrawal, Soumita Hait, and Amer E. Mouawad. On Finding Short Reconfiguration Sequences Between Independent Sets. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{agrawal_et_al:LIPIcs.ISAAC.2022.39,
  author =	{Agrawal, Akanksha and Hait, Soumita and Mouawad, Amer E.},
  title =	{{On Finding Short Reconfiguration Sequences Between Independent Sets}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{39:1--39:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.39},
  URN =		{urn:nbn:de:0030-drops-173244},
  doi =		{10.4230/LIPIcs.ISAAC.2022.39},
  annote =	{Keywords: Token sliding, token jumping, fixed-parameter tractability, combinatorial reconfiguration, shortest reconfiguration sequence}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.35
Sketching Approximability of (Weak) Monarchy Predicates

Authors: Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, Madhu Sudan, and Santhoshini Velusamy

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
We analyze the sketching approximability of constraint satisfaction problems on Boolean domains, where the constraints are balanced linear threshold functions applied to literals. In particular, we explore the approximability of monarchy-like functions where the value of the function is determined by a weighted combination of the vote of the first variable (the president) and the sum of the votes of all remaining variables. The pure version of this function is when the president can only be overruled by when all remaining variables agree. For every k ≥ 5, we show that CSPs where the underlying predicate is a pure monarchy function on k variables have no non-trivial sketching approximation algorithm in o(√n) space. We also show infinitely many weaker monarchy functions for which CSPs using such constraints are non-trivially approximable by O(log(n)) space sketching algorithms. Moreover, we give the first example of sketching approximable asymmetric Boolean CSPs. Our results work within the framework of Chou, Golovnev, Sudan, and Velusamy (FOCS 2021) that characterizes the sketching approximability of all CSPs. Their framework can be applied naturally to get a computer-aided analysis of the approximability of any specific constraint satisfaction problem. The novelty of our work is in using their work to get an analysis that applies to infinitely many problems simultaneously.
Cite as

Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, Madhu Sudan, and Santhoshini Velusamy. Sketching Approximability of (Weak) Monarchy Predicates. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chou_et_al:LIPIcs.APPROX/RANDOM.2022.35,
  author =	{Chou, Chi-Ning and Golovnev, Alexander and Shahrasbi, Amirbehshad and Sudan, Madhu and Velusamy, Santhoshini},
  title =	{{Sketching Approximability of (Weak) Monarchy Predicates}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.35},
  URN =		{urn:nbn:de:0030-drops-171573},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.35},
  annote =	{Keywords: sketching algorithms, approximability, linear threshold functions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.15
Galactic Token Sliding

Authors: Valentin Bartier, Nicolas Bousquet, and Amer E. Mouawad

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

Abstract
Given a graph G and two independent sets I_s and I_t of size k, the Independent Set Reconfiguration problem asks whether there exists a sequence of independent sets (each of size k) I_s = I₀, I₁, I₂, …, I_𝓁 = I_t such that each independent set is obtained from the previous one using a so-called reconfiguration step. Viewing each independent set as a collection of k tokens placed on the vertices of a graph G, the two most studied reconfiguration steps are token jumping and token sliding. In the Token Jumping variant of the problem, a single step allows a token to jump from one vertex to any other vertex in the graph. In the Token Sliding variant, a token is only allowed to slide from a vertex to one of its neighbors. Like the Independent Set problem, both of the aforementioned problems are known to be W[1]-hard on general graphs (for parameter k). A very fruitful line of research [Bodlaender, 1988; Grohe et al., 2017; Telle and Villanger, 2019; Pilipczuk and Siebertz, 2021] has showed that the Independent Set problem becomes fixed-parameter tractable when restricted to sparse graph classes, such as planar, bounded treewidth, nowhere-dense, and all the way to biclique-free graphs. Over a series of papers, the same was shown to hold for the Token Jumping problem [Ito et al., 2014; Lokshtanov et al., 2018; Siebertz, 2018; Bousquet et al., 2017]. As for the Token Sliding problem, which is mentioned in most of these papers, almost nothing is known beyond the fact that the problem is polynomial-time solvable on trees [Demaine et al., 2015] and interval graphs [Marthe Bonamy and Nicolas Bousquet, 2017]. We remedy this situation by introducing a new model for the reconfiguration of independent sets, which we call galactic reconfiguration. Using this new model, we show that (standard) Token Sliding is fixed-parameter tractable on graphs of bounded degree, planar graphs, and chordal graphs of bounded clique number. We believe that the galactic reconfiguration model is of independent interest and could potentially help in resolving the remaining open questions concerning the (parameterized) complexity of Token Sliding.
Cite as

Valentin Bartier, Nicolas Bousquet, and Amer E. Mouawad. Galactic Token Sliding. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bartier_et_al:LIPIcs.ESA.2022.15,
  author =	{Bartier, Valentin and Bousquet, Nicolas and Mouawad, Amer E.},
  title =	{{Galactic Token Sliding}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.15},
  URN =		{urn:nbn:de:0030-drops-169535},
  doi =		{10.4230/LIPIcs.ESA.2022.15},
  annote =	{Keywords: reconfiguration, independent set, galactic reconfiguration, sparse graphs, token sliding, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.44
Turbocharging Heuristics for Weak Coloring Numbers

Authors: Alexander Dobler, Manuel Sorge, and Anaïs Villedieu

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

Abstract
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which generalize the well-known graph invariant degeneracy (also called k-core number). Being NP-hard, weak-coloring numbers were previously computed on real-world graphs mainly via incremental heuristics. We study whether it is feasible to augment such heuristics with exponential-time subprocedures that kick in when a desired upper bound on the weak coloring number is breached. We provide hardness and tractability results on the corresponding computational subproblems. We implemented several of the resulting algorithms and show them to be competitive with previous approaches on a previously studied set of benchmark instances containing 86 graphs with up to 183831 edges. We obtain improved weak coloring numbers for over half of the instances.
Cite as

Alexander Dobler, Manuel Sorge, and Anaïs Villedieu. Turbocharging Heuristics for Weak Coloring Numbers. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dobler_et_al:LIPIcs.ESA.2022.44,
  author =	{Dobler, Alexander and Sorge, Manuel and Villedieu, Ana\"{i}s},
  title =	{{Turbocharging Heuristics for Weak Coloring Numbers}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{44:1--44:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.44},
  URN =		{urn:nbn:de:0030-drops-169820},
  doi =		{10.4230/LIPIcs.ESA.2022.44},
  annote =	{Keywords: Structural sparsity, parameterized algorithms, parameterized complexity, fixed-parameter tractability}
}
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