41 Search Results for "Gąsieniec, Leszek"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.13
Faster Algorithms for Shortest Unique or Absent Substrings

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) in a string S of length n. Both problems admit folklore 𝒪(n)-time solutions using the suffix tree of S. However, for small alphabets, this complexity is not necessarily optimal in the word RAM model, where a string of length n over alphabet [0,σ) can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We present an 𝒪(n log σ/√{log n})-time algorithm for computing a SUS in S. This algorithm decomposes the problem according to the length and the period of the sought substring and uses several tools and techniques, such as synchronizing sets, the analysis of runs, and wavelet trees, to reduce the computation of a SUS to a simple geometric problem. Further, we adapt this algorithm and combine it with an efficient construction of de Bruijn sequences in order to obtain an 𝒪(n log σ/√{log n})-time algorithm for computing a SAS in S.
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba. Faster Algorithms for Shortest Unique or Absent Substrings. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.SWAT.2026.13,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Pissis, Solon P. and Verbeek, Hilde and Zuba, Wiktor},
  title =	{{Faster Algorithms for Shortest Unique or Absent Substrings}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.13},
  URN =		{urn:nbn:de:0030-drops-260493},
  doi =		{10.4230/LIPIcs.SWAT.2026.13},
  annote =	{Keywords: string algorithms, unique substrings, absent substrings, absent words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.31
On the Smallest Size of Internal Collage Systems

Authors: Soichiro Migita, Kyotaro Uehata, and Tomohiro I

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
A Straight-Line Program (SLP) for a string T is a context-free grammar in Chomsky normal form that derives T only, which can be seen as a compressed form of T. Kida et al. introduced collage systems [Theor. Comput. Sci., 2003] to generalize SLPs by adding repetition rules and truncation rules. The smallest size c(T) of collage systems for T has gained attention to see how these generalized rules improve the compression ability of SLPs. Navarro et al. [IEEE Trans. Inf. Theory, 2021] showed that c(T) ∈ O(z(T)) and there is a string family with c(T) ∈ Ω(b(T) log |T|), where z(T) is the number of phrases in the Lempel-Ziv parsing of T and b(T) is the smallest size of bidirectional schemes for T. They also introduced a subclass of collage systems, called internal collage systems, and proved that its smallest size ĉ(T) for T is at least b(T). While c(T) ≤ ĉ(T) is obvious, it is unknown how large ĉ(T) is compared to c(T). In this paper, we prove that ĉ(T) = Θ(c(T)) by showing that any collage system of size m can be transformed into an internal collage system of size O(m) in O(m²) time. Thanks to this result, we can focus on internal collage systems to study the asymptotic behavior of c(T), which helps to suppress excess use of truncation rules. As a direct application, we get b(T) = O(c(T)), which answers an open question posed in [Navarro et al., IEEE Trans. Inf. Theory, 2021]. We also give a MAX-SAT formulation to compute ĉ(T) for a given T.
Cite as

Soichiro Migita, Kyotaro Uehata, and Tomohiro I. On the Smallest Size of Internal Collage Systems. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{migita_et_al:LIPIcs.CPM.2026.31,
  author =	{Migita, Soichiro and Uehata, Kyotaro and I, Tomohiro},
  title =	{{On the Smallest Size of Internal Collage Systems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.31},
  URN =		{urn:nbn:de:0030-drops-259575},
  doi =		{10.4230/LIPIcs.CPM.2026.31},
  annote =	{Keywords: Collage Systems, Dictionary-based compression, Compressibility measures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.24
Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics

Authors: Justine Cauvi, Nils Morawietz, and Laurent Viennot

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P. We consider the problems where the given property P is a prescribed matrix for the duration, length, or earliest arrival time of pairwise temporal paths. This means that we are given a matrix D and ask whether there is a temporal graph such that for any ordered pair of vertices (s,t), D_{s,t} equals the duration (length, or earliest arrival time, respectively) of any temporal path from s to t minimizing that specific temporal path metric. For shortest and earliest arrival temporal paths, we are the first to consider these problems as far as we know. We analyze these problems for many settings such as: strict and non-strict paths, periodic and non-periodic temporal graphs, and limited number of labels per edge (limited number of occurrences per edge over time). In contrast to all other path metrics, we show that for the earliest arrival times, we can achieve polynomial-time algorithms in periodic and non-periodic temporal graphs and for strict and and non-strict paths. However, the problem becomes NP-hard when the matrix does not contain a single integer but a set or range of possible allowed values. As we show, the problem can still be solved efficiently in this scenario, when the number of entries with more than one value is small, that is, we develop an FPT-algorithm for the number of such entries. For the setting of fastest paths, we achieve new hardness results that answers an open question by Klobas, Mertzios, Molter, and Spirakis [Theor. Comput. Sci. '25] about the parameterized complexity of the problem with respect to the vertex cover number and significantly improves over a previous hardness result for the feedback vertex set number. When considering shortest paths, we show that the periodic versions are polynomial-time solvable whereas the non-periodic versions become NP-hard.
Cite as

Justine Cauvi, Nils Morawietz, and Laurent Viennot. Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cauvi_et_al:LIPIcs.STACS.2026.24,
  author =	{Cauvi, Justine and Morawietz, Nils and Viennot, Laurent},
  title =	{{Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.24},
  URN =		{urn:nbn:de:0030-drops-255139},
  doi =		{10.4230/LIPIcs.STACS.2026.24},
  annote =	{Keywords: network design, temporal paths, foremost paths, fastest paths, shortest paths, non-strict paths, periodic temporal graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.18
Optimal Deterministic Rendezvous in Labeled Lines

Authors: Yann Bourreau, Ananth Narayanan, and Alexandre Nolin

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In a rendezvous task, a set of mobile agents initially dispersed in a network have to gather at an arbitrary common site. We consider the rendezvous problem on the infinite labeled line, with 2 initially asleep agents, without communication, and a synchronous notion of time. Each node on the line is labeled with a unique positive integer. The initial distance between the two agents is denoted by D. Time is divided into rounds and measured from the moment an agent first wakes up. We denote by τ the delay between the two agents' wake up times. If awake in a given round T, an agent at a node v has three options: stay at the node v, take port 0, or take port 1. If it decides to stay, the agent will still be at node v in round T+1. Otherwise, it will be at one of the two neighbors of v on the infinite line, depending on the port it chose. The agents achieve rendezvous in T rounds if they are at the same node in round T. We aim for a deterministic algorithm for this problem. The problem was recently considered by Miller and Pelc [Distributed Computing, 2025]. With 𝓁_{max} the largest label of the two starting nodes, they showed that no algorithm can guarantee rendezvous in o(D log^* 𝓁_{max}) rounds. The lower bound follows from a connection with the LOCAL model of distributed computing, and holds even if the agents are guaranteed simultaneous wake-up (τ = 0) and are told their initial distance D. Miller and Pelc also gave an algorithm of optimal matching complexity O(D log^* 𝓁_{max}) when the agents know D, but only obtained the higher bound of O(D² (log^* 𝓁_{max})³) when D is unknown to the agents. In this paper, we improve this second complexity to a tight O(D log^* 𝓁_{max}), closing the gap between the best known lower and upper bounds. In fact, our algorithm achieves rendezvous in O(D log^* 𝓁_{min}) rounds, where 𝓁_{min} is the smallest label within distance O(D) of the two starting positions. We obtain this result by having the agents compute sparse subsets of the nodes to gather at (formally, ruling sets over the line), as well as some general observations about the setting of rendezvous on labeled graphs.
Cite as

Yann Bourreau, Ananth Narayanan, and Alexandre Nolin. Optimal Deterministic Rendezvous in Labeled Lines. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bourreau_et_al:LIPIcs.STACS.2026.18,
  author =	{Bourreau, Yann and Narayanan, Ananth and Nolin, Alexandre},
  title =	{{Optimal Deterministic Rendezvous in Labeled Lines}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.18},
  URN =		{urn:nbn:de:0030-drops-255071},
  doi =		{10.4230/LIPIcs.STACS.2026.18},
  annote =	{Keywords: mobile agents, rendezvous, ruling set, deterministic algorithms, labeled line}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.30
Byzantine-Tolerant Phase Clock

Authors: Costas Busch, Paweł Garncarek, and Dariusz R. Kowalski

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
A phase clock is a basic synchronization mechanism that keeps distributed nodes closely synchronized to execute the same phase of a distributed algorithm. A phase clock is typically implemented with a local logical counter that keeps track of the current phase count. Phase clocks are particularly useful in population protocols for implementing leader election and majority selection. We study phase clocks that tolerate Byzantine faults. We show that there is a phase clock that tolerates up to f < n/3 faulty nodes, where n is the number of nodes, such that the gap of the local counter values is O(n²log n). The gap can be further lowered to O(log n) when f ≤ n/8. We also show that if f > n/3, then the gap grows to infinity as time increases. While analyzing phase clock we introduce novel techniques and bounds for balls into bins processes, which might be of independent interest. Using the phase clock, we obtain a majority selection population protocol that tolerates up to f faults and decides on the majority value in O(log² n) parallel time using poly-log states per node.
Cite as

Costas Busch, Paweł Garncarek, and Dariusz R. Kowalski. Byzantine-Tolerant Phase Clock. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{busch_et_al:LIPIcs.OPODIS.2025.30,
  author =	{Busch, Costas and Garncarek, Pawe{\l} and Kowalski, Dariusz R.},
  title =	{{Byzantine-Tolerant Phase Clock}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.30},
  URN =		{urn:nbn:de:0030-drops-252036},
  doi =		{10.4230/LIPIcs.OPODIS.2025.30},
  annote =	{Keywords: phase clock, Byzantine nodes, population protocols, balls into bins}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.14
Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks

Authors: Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
We consider two fundamental communication tasks in arbitrary radio networks: broadcasting (information from one source has to reach all nodes) and gossiping (every node has a message and all messages have to reach all nodes). Nodes are assigned labels that are (not necessarily different) binary strings. Each node knows its own label and can use it as a parameter in the same deterministic algorithm. The length of a labeling scheme is the largest length of a label. The goal is to find labeling schemes of asymptotically optimal length for the above tasks, and to design fast deterministic distributed algorithms for each of them, using labels of optimal length. Our main result concerns broadcasting. We show the existence of a labeling scheme of constant length that supports broadcasting in time O(D+log² n), where D is the diameter of the network and n is the number of nodes. This broadcasting time is an improvement over the best currently known O(Dlog n + log² n) time of broadcasting with constant-length labels, due to Ellen and Gilbert (SPAA 2020). It also matches the optimal broadcasting time in radio networks of known topology. Hence, we show that appropriately chosen node labels of constant length permit to achieve, in a distributed way, the optimal centralized broadcasting time. This is, perhaps, the most surprising finding of this paper. We are able to obtain our result thanks to a novel methodological tool of propagating information in radio networks, that we call a 2-height respecting tree. Next, we apply our broadcasting algorithm to solve the gossiping problem. We get a gossiping algorithm working in time O(D + Δlog n + log² n), using a labeling scheme of optimal length O(log Δ), where Δ is the maximum degree. Our time is the same as the best known gossiping time in radio networks of known topology.
Cite as

Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc. Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganczorz_et_al:LIPIcs.OPODIS.2025.14,
  author =	{Ganczorz, Adam and Jurdzinski, Tomasz and Pelc, Andrzej},
  title =	{{Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.14},
  URN =		{urn:nbn:de:0030-drops-251874},
  doi =		{10.4230/LIPIcs.OPODIS.2025.14},
  annote =	{Keywords: radio network, distributed algorithms, algorithms with advice, labeling scheme, broadcasting, gossiping}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.47
Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems

Authors: Yusuke Kobayashi and Bingkai Lin

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the Pinwheel Packing problem, we are given a set of recurring tasks, each associated with a positive integer a_i for task i. The objective is to select one task to perform each day such that every task i is performed at least once within every a_i consecutive days. The exact computational complexity of this problem, where ∑ 1/a_i = 1, has remained an open question for more than 30 years; in particular, it is still unknown whether the problem is NP-hard. The first contribution of this paper is to show that Pinwheel Packing cannot be solved in polynomial time under a standard complexity assumption, improving upon the hardness result shown by Jacobs and Longo. Additionally, we present fixed-parameter algorithms for variants of Pinwheel Packing, parameterized by the number of tasks.
Cite as

Yusuke Kobayashi and Bingkai Lin. Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 47:1-47:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2025.47,
  author =	{Kobayashi, Yusuke and Lin, Bingkai},
  title =	{{Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{47:1--47:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.47},
  URN =		{urn:nbn:de:0030-drops-249558},
  doi =		{10.4230/LIPIcs.ISAAC.2025.47},
  annote =	{Keywords: Pinwheel Scheduling, Polynomial-time Solvability, Packing and Covering, Fixed Parameter Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.17
Realization of Temporally Connected Graphs Based on Degree Sequences

Authors: Arnaud Casteigts, Michelle Döring, and Nils Morawietz

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Given an undirected graph G, the problem of deciding whether G admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (Göbel et al., 1991). In this article, we relax this problem and ask whether a given degree sequence can be realized as a temporally connected graph. Our main results are a complete characterization of the feasible cases, and a recognition algorithm that runs in 𝒪(n) time for graphical degree sequences (realized as simple temporal graphs) and in 𝒪(n+m) time for multigraphical degree sequences (realized as non-simple temporal graphs, where the number of time labels on an edge corresponds to the multiplicity of the edge in the multigraph). In fact, these algorithms can be made constructive at essentially no cost. Namely, we give a constructive 𝒪(n+m) time algorithm that outputs, for a given (multi)graphical degree sequence 𝐝, a temporally connected graph whose underlying (multi)graph is a realization of 𝐝, if one exists.
Cite as

Arnaud Casteigts, Michelle Döring, and Nils Morawietz. Realization of Temporally Connected Graphs Based on Degree Sequences. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{casteigts_et_al:LIPIcs.ISAAC.2025.17,
  author =	{Casteigts, Arnaud and D\"{o}ring, Michelle and Morawietz, Nils},
  title =	{{Realization of Temporally Connected Graphs Based on Degree Sequences}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.17},
  URN =		{urn:nbn:de:0030-drops-249256},
  doi =		{10.4230/LIPIcs.ISAAC.2025.17},
  annote =	{Keywords: temporal paths, gossiping, (multi)graphical degree sequences, edge-disjoint spanning trees, linear time algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.27
Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs

Authors: Michelle Döring

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Temporal graphs model networks whose connections are available only at specific points in time. Several definitional subtleties - whether paths must follow strictly increasing time labels (strict vs. non-strict), whether adjacent edges cannot appear simultaneously (proper), and whether edges are forbidden to appear multiple times (simple) - give rise to different temporal graph settings. These distinctions directly impact the definition of temporal reachability, a core concept in temporal graph theory. Casteigts, Corsini, and Sarkar [TCS24] introduced a framework of equivalence notions to compare the expressive power of these settings focusing solely on undirected temporal graphs. In this work, we extend their framework to include the fundamental dimension of directed vs. undirected. Our contribution is three-fold. We (1) complete the undirected hierarchy by resolving the two open questions from [TCS24], (2) fully characterize the hierarchy of the directed settings, and (3) compare the directed and undirected settings, showing that directed temporal graphs are strictly more expressive than undirected temporal graphs in terms of reachability. Our structural results highlight both the limitations and strengths of various temporal graph settings - for example, directed + strict + simple graphs can realize every possible reachability graph, while directed + proper graphs necessarily induce at least one transitive reachability on each directed cycle. We also provide transformation procedures between temporal settings offering practical tools for transferring algorithms and hardness results across models.
Cite as

Michelle Döring. Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doring:LIPIcs.ISAAC.2025.27,
  author =	{D\"{o}ring, Michelle},
  title =	{{Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.27},
  URN =		{urn:nbn:de:0030-drops-249353},
  doi =		{10.4230/LIPIcs.ISAAC.2025.27},
  annote =	{Keywords: temporal graphs, directed graphs, temporal reachability, dynamic networks}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.34
Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice

Authors: Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Radio Networks (RN) is one of the fundamental models for network communication where nodes can broadcast messages locally but their simultaneous transmissions can interfere with each other at their shared neighbors. This work focuses on performing the very fundamental primitive of Local Broadcast, in spite of the interferences. We investigate to what extent local knowledge, called advice, relating to the 2-local domination number γ₂ may speed up Local Broadcast. Specifically for each node and some dominating set, knowledge about some neighboring dominating node and the local number among the neighbors of that dominating node. We show that such advice is sufficient to build an efficient oblivious transmission schedule. Along those lines, we present three algorithms trading the level of adaptiveness (from oblivious to adaptive) for bits of advice per node (from O(log (Δγ₂)) to 1). All our algorithms complete Local Broadcast in Õ(Δγ₂²) rounds, where Δ is the maximum degree of the network. On the side of lower bounds, we show that, for each quasi-adaptive deterministic Local Broadcast algorithm, there is some RN that requires Ω(min{(min{Δ,γ₂}/log n)²,n}) communication rounds, where n is the number of network nodes. In quasi-adaptive protocols nodes may stop executing once its computational task is completed. To the best of our knowledge, this is the first (nearly) quadratic Local Broadcast (same message for all neighbors) lower bound in the RN model. Our lower bound is stronger than previous works in multiple ways: i) it is nearly quadratically better than the best known general lower bound for this class of algorithms, ii) it applies to a wider class of algorithms than previous work for fully oblivious, iii) it achieves similar time lower bound than previous work proved for a much more demanding Local Broadcast where each node sends a possibly different message to each neighbor, and iv) it takes into account the local domination parameter γ₂.
Cite as

Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garncarek_et_al:LIPIcs.ISAAC.2025.34,
  author =	{Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R. and Kutten, Shay and Mosteiro, Miguel A.},
  title =	{{Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.34},
  URN =		{urn:nbn:de:0030-drops-249426},
  doi =		{10.4230/LIPIcs.ISAAC.2025.34},
  annote =	{Keywords: Radio Networks, Local Broadcast, Distributed Deterministic Algorithms, Lower Bounds, Graph algorithms, Advice, Labeling Schemes, Local Domination}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.35
Anonymous Self-Stabilising Localisation via Spatial Population Protocols

Authors: Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the distributed localisation problem (DLP), n anonymous robots (agents) A_0, ..., A_{n-1} are located at arbitrary points p_0, ..., p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified (jointly agreed) coordinate system, in which all agents receive unique labels (coordinates) that accurately reflect the relative distances between all points p_0, ..., p_{n-1} in S. Extensive research on DLP has primarily focus on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In contrast, this paper proposes a minimalist, computationally efficient distributed computing model where agents can query any pairwise relative positions, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v_{ij} spanning points p_i and p_j (vector query model). We propose and analyse several distributed localisation protocols, including: 1) Leader-based localisation protocol with distance queries We propose and analyse two leader-based localisation protocols that stabilise silently in o(n) time. These protocols leverage an efficient solution to the novel concept of multi-contact epidemic, a natural generalisation of the core communication tool in population protocols, known as the one-way epidemic. 2) Self-stabilising leader localisation protocol with distance queries We show how to effectively utilise a leader election mechanism within the leader-based localisation protocol to get a DLP protocol that self-stabilises silently in time O(n(log n/n)^{1/(k+1)}log n) in k-dimensions. 3) Self-stabilising localisation protocol with vector queries We propose and analyse an optimally fast DLP protocol which self-stabilises silently in O(log n) time.
Cite as

Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Anonymous Self-Stabilising Localisation via Spatial Population Protocols. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gasieniec_et_al:LIPIcs.ISAAC.2025.35,
  author =	{G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Anonymous Self-Stabilising Localisation via Spatial Population Protocols}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.35},
  URN =		{urn:nbn:de:0030-drops-249433},
  doi =		{10.4230/LIPIcs.ISAAC.2025.35},
  annote =	{Keywords: Population Protocols, Distributed Localisation, Spacial Queries, Self-Stabilisation}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.30
Team Formation and Applications

Authors: Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph, using bounded size messages, where a certain fraction of the nodes may experience a generalized, strictly stronger, version of initial failures. The goal of a TF algorithm is to assemble tokens injected by the environment, in a distributed manner, into teams of size σ, where σ is a parameter of the problem. The usefulness of TF is demonstrated by using it to derive efficient algorithms for many distributed problems. Specifically, we show that various (one-shot as well as long-lived) distributed problems reduce to TF. This includes well-known (and extensively studied) distributed problems such as several versions of leader election and threshold detection. For example, we are the first to break the linear message complexity bound for asynchronous implicit leader election. We also improve the time complexity of message-optimal algorithms for asynchronous explicit leader election. Other distributed problems that reduce to TF are new ones, including matching players in online gaming platforms, a generalization of gathering, constructing a perfect matching in an induced subgraph of the complete graph, and more. To complement our positive contribution, we establish a tight lower bound on the message complexity of TF algorithms.
Cite as

Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld. Team Formation and Applications. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 30:1-30:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{emek_et_al:LIPIcs.DISC.2025.30,
  author =	{Emek, Yuval and Kutten, Shay and Rafael, Ido and Taubenfeld, Gadi},
  title =	{{Team Formation and Applications}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{30:1--30:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.30},
  URN =		{urn:nbn:de:0030-drops-248474},
  doi =		{10.4230/LIPIcs.DISC.2025.30},
  annote =	{Keywords: asynchronous message-passing, complete communication graph, initial failures, leader election, matching}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.33
Approach of Agents with Restricted Fuel Tanks

Authors: Adam Ganczorz, Tomasz Jurdzinski, Andrzej Pelc, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
Two mobile agents, modelled as points in the plane moving at speed 1, have to get at a distance at most 1 from each other. This task is known as approach or rendezvous in the plane. An adversary initially places both agents at distinct points, called their bases, at distance at most D, and wakes them up at possibly different times. Each of the agents has a fuel tank that allows them to traverse a trajectory of length D, and can be replenished at the base of the agent. The algorithm of each agent consists of a series of actions which are either moves at a chosen distance in a chosen direction or staying idle for a chosen period of time. For a given instance of the approach task, the execution time of an approach algorithm is the length of the period between the start of the later agent and the moment of approach. Our goal is to design approach algorithms with optimal time complexity. We consider two independent coherence assumptions. One of them is time coherence, i.e., agents start simultaneously, and the other is orientation coherence: agents have compatible compasses, showing the same North direction. Our main result is establishing optimal time complexity of the approach problem with restricted fuel tanks. It turns out that this optimal complexity heavily depends on the above coherence assumptions. If both of them are satisfied then approach can be performed in time O(D²) and we show that this complexity is optimal. If any of the two coherence assumptions is missing then approach can be performed in time O(D²√D) and we prove that this order of magnitude cannot be improved. Our main technical contribution are lower bounds showing that, for each of the considered scenarios, our fairly natural approach algorithms are, in fact, optimal.
Cite as

Adam Ganczorz, Tomasz Jurdzinski, Andrzej Pelc, and Grzegorz Stachowiak. Approach of Agents with Restricted Fuel Tanks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2025.33,
  author =	{Ganczorz, Adam and Jurdzinski, Tomasz and Pelc, Andrzej and Stachowiak, Grzegorz},
  title =	{{Approach of Agents with Restricted Fuel Tanks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{33:1--33:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.33},
  URN =		{urn:nbn:de:0030-drops-248506},
  doi =		{10.4230/LIPIcs.DISC.2025.33},
  annote =	{Keywords: mobile agent, approach, rendezvous, plane, restricted energy}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.58
Brief Announcement: Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks

Authors: Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We consider two fundamental communication tasks in arbitrary radio networks: broadcasting (information from one source has to reach all nodes) and gossiping (every node has a message and all messages have to reach all nodes). Nodes are assigned labels that are (not necessarily different) binary strings. Each node knows its own label and can use it as a parameter in the same deterministic algorithm. The length of a labeling scheme is the largest length of a label. The goal is to find labeling schemes of asymptotically optimal length for the above tasks, and to design fast deterministic distributed algorithms for each of them, using labels of optimal length. Our main result concerns broadcasting. We show the existence of a labeling scheme of constant length that supports broadcasting in time O(D+log² n), where D is the diameter of the network and n is the number of nodes. This broadcasting time is an improvement over the best currently known O(Dlog n + log² n) time of broadcasting with constant-length labels, due to Ellen and Gilbert (SPAA 2020). It also matches the optimal broadcasting time in radio networks of known topology. Hence, we show that appropriately chosen node labels of constant length permit to achieve, in a distributed way, the optimal centralized broadcasting time. This is, perhaps, the most surprising finding of this paper. We are able to obtain our result thanks to a novel methodological tool of propagating information in radio networks, that we call a 2-height respecting tree. Next, we apply our broadcasting algorithm to solve the gossiping problem. We get a gossiping algorithm working in time O(D + Δlog n + log² n), using a labeling scheme of optimal length O(log Δ), where Δ is the maximum degree. Our time is the same as the best known gossiping time in radio networks of known topology.
Cite as

Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc. Brief Announcement: Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 58:1-58:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2025.58,
  author =	{Ganczorz, Adam and Jurdzinski, Tomasz and Pelc, Andrzej},
  title =	{{Brief Announcement: Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{58:1--58:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.58},
  URN =		{urn:nbn:de:0030-drops-248744},
  doi =		{10.4230/LIPIcs.DISC.2025.58},
  annote =	{Keywords: radio network, distributed algorithms, algorithms with advice, labeling scheme, broadcasting, gossiping}
}
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