13 Search Results for "Oostveen, Jelle J."

Document
DOI: 10.4230/LIPIcs.STACS.2026.73
Colouring Probe H-Free Graphs

Authors: Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen

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

Abstract
The NP-complete problems Colouring and k-Colouring (k ≥ 3) are well studied on H-free graphs, i.e., graphs that do not contain some fixed graph H as an induced subgraph. We research to what extent the known polynomial-time algorithms for H-free graphs can be generalized if we only know some of the edges of the input graph. We do this by considering the classical probe graph model introduced in the early nineties. For a graph H, a partitioned probe H-free graph (G,P,N) consists of a graph G = (V,E), together with a set P ⊆ V of probes and an independent set N = V ⧵ P of non-probes, such that G+F is H-free for some edge set F ⊆ binom(N,2). We show the following: - We fully classify Colouring on partitioned probe H-free graphs and show that the obtained complexity dichotomy differs from the known dichotomy of Colouring for H-free graphs. - We fully classify 3-Colouring on partitioned probe P_t-free graphs: we prove polynomial-time solvability for t ≤ 5 and NP-completeness for t ≥ 6. In contrast, 3-Colouring on P_t-free graphs is known to be polynomial-time solvable for t ≤ 7 and quasi-polynomial-time solvable for t ≥ 8. Our main result is our polynomial-time algorithm for 3-Colouring on partitioned P₅-free graphs. For this result, and also for all our other polynomial-time results, we do not need to know the edge set F; we only need to know its existence. Moreover, the class of probe P₅-free graphs includes not only paths of arbitrary length but even all bipartite graphs and is much richer than the class of P₅-free graphs. The latter is also evidenced by the fact that there exist graph problems, such as Matching Cut, that are known to be polynomial-time solvable for P₅-free graphs but NP-complete for partitioned probe P₅-free graphs. In particular, unlike the class of 3-colourable P₅-free graphs, the class of 3-colourable probe P₅-free graphs has unbounded mim-width. Hence, our polynomial-time result for 3-Colouring for probe P₅-free graphs suggests that there may be another, deeper overarching reason why 3-Colouring is polynomial-time solvable for P₅-free graphs.
Cite as

Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen. Colouring Probe H-Free Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paulusma_et_al:LIPIcs.STACS.2026.73,
  author =	{Paulusma, Dani\"{e}l and Rauch, Johannes and van Leeuwen, Erik Jan},
  title =	{{Colouring Probe H-Free Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{73:1--73:20},
  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.2026.73},
  URN =		{urn:nbn:de:0030-drops-255621},
  doi =		{10.4230/LIPIcs.STACS.2026.73},
  annote =	{Keywords: colouring, probe graph, forbidden induced subgraph, complexity dichotomy}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.4
Unit Interval Selection in Random Order Streams

Authors: Cezar-Mihail Alexandru, Adithya Diddapur, Magnús M. Halldórsson, Christian Konrad, and Kheeran K. Naidu

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

Abstract
We consider the Unit Interval Selection problem in the one-pass random order streaming model. In this setting, an algorithm is presented with a sequence of n unit-length intervals on the line that arrive in uniform random order, one at a time, and the objective is to output (an approximation of) a largest set of disjoint intervals using space linear in the size of an optimal solution. Previous work only considered adversarially ordered streams and established that, within these space constraints, a (2/3)-approximation can be achieved in such streams, and this is best possible, in that going beyond such an approximation factor requires space Ω(n) [Emek et al., TALG'16]. In this work, we show that an improved expected approximation factor can be achieved if the input stream is in uniform random order, where the expectation is taken over the stream order. More specifically, we give a one-pass streaming algorithm with expected approximation factor 0.7401 that uses space O(|OPT|), where OPT denotes an optimal solution. We also show that random order algorithms with expected approximation factor above 8/9 require space Ω(n), and algorithms that compute a better than 2/3-approximation with probability above 2/3 also require Ω(n) space. On a technical level, we design an algorithm for the restricted domain [0, Δ), for some constant Δ, and use standard techniques to obtain an algorithm for unrestricted domains. For the restricted domain [0, Δ), we run O(Δ) recursive instances of our algorithm, with each instance targeting the situation where a specific interval of an optimal solution arrives first. We establish the interesting property of our algorithm that it performs worst when the input stream consists solely of a set of independent intervals. It then remains to analyse the algorithm on these simple instances. Our lower bound is proved via communication complexity arguments, similar in spirit to the robust communication lower bounds established by [Chakrabarti et al., Theory Comput. 2016].
Cite as

Cezar-Mihail Alexandru, Adithya Diddapur, Magnús M. Halldórsson, Christian Konrad, and Kheeran K. Naidu. Unit Interval Selection in Random Order Streams. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alexandru_et_al:LIPIcs.STACS.2026.4,
  author =	{Alexandru, Cezar-Mihail and Diddapur, Adithya and Halld\'{o}rsson, Magn\'{u}s M. and Konrad, Christian and Naidu, Kheeran K.},
  title =	{{Unit Interval Selection in Random Order Streams}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{4:1--4:20},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-254933},
  doi =		{10.4230/LIPIcs.STACS.2026.4},
  annote =	{Keywords: Random order streaming algorithms, unit interval selection}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.51
Structural Parameterization of Steiner Tree Packing

Authors: Niko Hastrich and Kirill Simonov

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

Abstract
Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms. In this paper, we show the first FPT algorithms for STP parameterized by structural parameters of the input graph. In particular, we show that STP is fixed-parameter tractable by the tree-cut width as well as the fracture number of the input graph. To achieve our results, we generalize techniques from Edge-Disjoint Paths (EDP) to Generalized Steiner Tree Packing (GSTP), which generalizes both STP and EDP. First, we derive the notion of the augmented graph for GSTP analogous to EDP. We then show that GSTP is FPT by - the tree-cut width of the augmented graph, - the fracture number of the augmented graph, - the slim tree-cut width of the input graph. The latter two results were previously known for EDP; our results generalize these to GSTP and improve the running time for the parameter fracture number. On the other hand, it was open whether EDP is FPT parameterized by the tree-cut width of the augmented graph, despite extensive research on the structural complexity of the problem. We settle this question affirmatively.
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Niko Hastrich and Kirill Simonov. Structural Parameterization of Steiner Tree Packing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hastrich_et_al:LIPIcs.STACS.2026.51,
  author =	{Hastrich, Niko and Simonov, Kirill},
  title =	{{Structural Parameterization of Steiner Tree Packing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{51:1--51:18},
  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.2026.51},
  URN =		{urn:nbn:de:0030-drops-255405},
  doi =		{10.4230/LIPIcs.STACS.2026.51},
  annote =	{Keywords: Steiner tree packing, structural parameters, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.1
Triangle Detection in H-Free Graphs

Authors: Amir Abboud, Ron Safier, and Nathan Wallheimer

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate the study of combinatorial algorithms for Triangle Detection in H-free graphs. The goal is to decide if a graph that forbids a fixed pattern H as a subgraph contains a triangle, using only "combinatorial" methods that notably exclude fast matrix multiplication. Our work aims to classify which patterns admit a subcubic speedup, working towards a dichotomy theorem. On the lower bound side, we show that if H is not 3-colorable or contains more than one triangle, the complexity of the problem remains unchanged, and no combinatorial speedup is likely possible. On the upper bound side, we develop an embedding approach that results in a strongly subcubic, combinatorial algorithm for a rich class of "embeddable" patterns. Specifically, for an embeddable pattern of size k, our algorithm runs in Õ(n^{3-1/(2^{k-3)}}) time, where Õ(⋅) hides poly-logarithmic factors. This algorithm also extends to listing all the triangles within the same time bound. We supplement this main result with two generalizations: - A generalization to patterns that are embeddable up to a single obstacle that arises from a triangle in the pattern. This completes our classification for small patterns, yielding a dichotomy theorem for all patterns of size up to eight. - An H-sensitive algorithm for embeddable patterns, which runs faster when the number of copies of H is significantly smaller than the maximum possible Ω(n^{k}). Finally, we focus on the special case of odd cycles. We present specialized Triangle Detection algorithms that are very efficient: - A combinatorial algorithm for C_{2k+1}-free graphs that runs in Õ(m+n^{1+2/k}) time for every k ≥ 2, where m is the number of edges in the graph. - A combinatorial C₅-sensitive algorithm that runs in Õ(n² + n^{4/3} t^{1/3}) time, where t is the number of 5-cycles in the graph.
Cite as

Amir Abboud, Ron Safier, and Nathan Wallheimer. Triangle Detection in H-Free Graphs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{abboud_et_al:LIPIcs.ITCS.2026.1,
  author =	{Abboud, Amir and Safier, Ron and Wallheimer, Nathan},
  title =	{{Triangle Detection in H-Free Graphs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.1},
  URN =		{urn:nbn:de:0030-drops-252885},
  doi =		{10.4230/LIPIcs.ITCS.2026.1},
  annote =	{Keywords: fine-grained complexity, triangle detection, H-free graphs}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.17
Dynamic Streaming Algorithms for Geometric Independent Set

Authors: Timothy M. Chan and Yuancheng Yu

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We present the first space-efficient, fully dynamic streaming algorithm for computing a constant-factor approximation of the maximum independent set size of n axis-aligned rectangles in two dimensions. For an arbitrarily small constant δ > 0, our algorithm obtains an O((1/δ)²) approximation and requires O(U^δ polylog n) space and update time with high probability, assuming that coordinates are integers bounded by U. We also obtain a similar result for fat objects in any constant dimension. This extends recent non-streaming algorithms by Bhore and Chan from SODA'25, and also greatly extends previous streaming results, which were limited to special types of geometric objects such as one-dimensional intervals and unit disks.
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Timothy M. Chan and Yuancheng Yu. Dynamic Streaming Algorithms for Geometric Independent Set. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chan_et_al:LIPIcs.WADS.2025.17,
  author =	{Chan, Timothy M. and Yu, Yuancheng},
  title =	{{Dynamic Streaming Algorithms for Geometric Independent Set}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.17},
  URN =		{urn:nbn:de:0030-drops-242481},
  doi =		{10.4230/LIPIcs.WADS.2025.17},
  annote =	{Keywords: Geometric Independent Set, Dynamic Streaming Algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.18
Parameterized Streaming Algorithms for Topological Sorting

Authors: Ho-Lin Chen, Peng-Ting Lin, and Meng-Tsung Tsai

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Computing a topological ordering for an n-node directed acyclic graph (DAG) G is computationally challenging in streaming models. Chakrabarti et al. {[}SODA 2020{]} showed that in the insertion-only streaming model, every single-pass algorithm requires Ω(n²) space, and every k-pass algorithm requires n^{1+Ω(1/k)} space for any constant k ≥ 1. We study the parameterized complexity of streaming algorithms for topological sorting, considering two parameters: the independence number α and the maximum displacement δ. Our results include an O(1/ε)-pass O(α n^{1+ε})-space streaming algorithm and an O(n^{1/2})-pass O(n+δ²)-space streaming algorithm. For dense random DAGs, both α and δ are small, allowing us to improve the state-of-the-art for topological sorting in random DAGs. As applications, we show that strongly connected components (SCC) decomposition and 2-satisfiability (2-SAT) can be solved in O(1/ε) passes using O(α n^{1+ε}) space and O(α_I n^{1+ε}) space, respectively, where α_I denotes the independence number of the implication graph induced by the input 2-SAT instance.
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Ho-Lin Chen, Peng-Ting Lin, and Meng-Tsung Tsai. Parameterized Streaming Algorithms for Topological Sorting. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.WADS.2025.18,
  author =	{Chen, Ho-Lin and Lin, Peng-Ting and Tsai, Meng-Tsung},
  title =	{{Parameterized Streaming Algorithms for Topological Sorting}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.18},
  URN =		{urn:nbn:de:0030-drops-242495},
  doi =		{10.4230/LIPIcs.WADS.2025.18},
  annote =	{Keywords: Independence Number, Chain Cover, SCC Decomposition, 2-Satisfiability}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.33
A Min-Entropy Approach to Multi-Party Communication Lower Bounds

Authors: Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Information complexity is one of the most powerful techniques to prove information-theoretical lower bounds, in which Shannon entropy plays a central role. Though Shannon entropy has some convenient properties, such as the chain rule, it still has inherent limitations. One of the most notable barriers is the square-root loss, which appears in the square-root gap between entropy gaps and statistical distances, e.g., Pinsker’s inequality. To bypass this barrier, we introduce a new method based on min-entropy analysis. Building on this new method, we prove the following results. - An Ω(N^{∑_i α_i - max_i {α_i}}/k) randomized communication lower bound of the k-party set-intersection problem where the i-th party holds a random set of size ≈ N^{1-α_i}. - A tight Ω(n/k) randomized lower bound of the k-party Tree Pointer Jumping problems, improving an Ω(n/k²) lower bound by Chakrabarti, Cormode, and McGregor (STOC 08). - An Ω(n/k+√n) lower bound of the Chained Index problem, improving an Ω(n/k²) lower bound by Cormode, Dark, and Konrad (ICALP 19). Since these problems served as hard problems for numerous applications in streaming lower bounds and cryptography, our new lower bounds directly improve these streaming lower bounds and cryptography lower bounds. On the technical side, min-entropy does not have nice properties such as the chain rule. To address this issue, we enhance the structure-vs-pseudorandomness decomposition used by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24); both papers used this decomposition to prove communication lower bounds. In this paper, we give a new breath to this method in the multi-party setting, presenting a new toolkit for proving multi-party communication lower bounds.
Cite as

Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang. A Min-Entropy Approach to Multi-Party Communication Lower Bounds. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 33:1-33:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.CCC.2025.33,
  author =	{Huang, Mi-Ying (Miryam) and Mao, Xinyu and Wang, Shuo and Yang, Guangxu and Zhang, Jiapeng},
  title =	{{A Min-Entropy Approach to Multi-Party Communication Lower Bounds}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{33:1--33:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.33},
  URN =		{urn:nbn:de:0030-drops-237273},
  doi =		{10.4230/LIPIcs.CCC.2025.33},
  annote =	{Keywords: communication complexity, lifting theorems, set intersection, chained index}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.135
Deterministic Independent Sets in the Semi-Streaming Model

Authors: Daniel Ye

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We consider the independent set problem in the semi-streaming model. For any input graph G = (V, E) with n vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, G is presented as a stream of edges and any algorithm must use Õ(n) bits of memory to output a large independent set at the end of the stream. Prior work has designed various semi-streaming algorithms for finding independent sets. Due to the hardness of finding maximum and maximal independent sets in the semi-streaming model, the focus has primarily been on finding independent sets in terms of certain parameters, such as the maximum degree Δ. In particular, there is a simple randomized algorithm that obtains independent sets of size n/(Δ+1) in expectation, which can also be achieved with high probability using more complicated algorithms. For deterministic algorithms, the best bounds are significantly weaker. The best we know is a straightforward algorithm that finds an Ω̃(n/(Δ²)) size independent set. We show that this straightforward algorithm is nearly optimal by proving that any deterministic semi-streaming algorithm can only output an Õ(n/(Δ²)) size independent set. Our result proves a strong separation between the power of deterministic and randomized semi-streaming algorithms for the independent set problem.
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Daniel Ye. Deterministic Independent Sets in the Semi-Streaming Model. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 135:1-135:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ye:LIPIcs.ICALP.2025.135,
  author =	{Ye, Daniel},
  title =	{{Deterministic Independent Sets in the Semi-Streaming Model}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{135:1--135:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.135},
  URN =		{urn:nbn:de:0030-drops-235129},
  doi =		{10.4230/LIPIcs.ICALP.2025.135},
  annote =	{Keywords: Sublinear Algorithms, Derandomization, Semi-Streaming Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.89
Optimal Communication Complexity of Chained Index

Authors: Janani Sundaresan

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We study the chain communication problem introduced by Cormode et al. [ICALP 2019]. For k ≥ 1, in the chain_{n,k} problem, there are k string and index pairs (X_i, σ_i) for i ∈ [k] such that the value at position σ_i in string X_i is the same bit for all k pairs. The input is shared between k+1 players as follows. Player 1 has the first string X₁ ∈ {0,1}ⁿ, player 2 has the first index σ₁ ∈ [n] and the second string X₂ ∈ {0,1}ⁿ, player 3 has the second index σ₂ ∈ [n] along with the third string X₃ ∈ {0,1}ⁿ, and so on. Player k+1 has the last index σ_k ∈ [n]. The communication is one way from each player to the next, starting from player 1 to player 2, then from player 2 to player 3 and so on. Player k+1, after receiving the message from player k, has to output a single bit which is the value at position σ_i in X_i for any i ∈ [k]. It is a generalization of the well-studied index problem, which is equivalent to chain_{n, 2}. Cormode et al. proved that the chain_{n,k} problem requires Ω(n/k²) communication, and they used it to prove streaming lower bounds for the approximation of maximum independent sets. Subsequently, Feldman et al. [STOC 2020] used it to prove lower bounds for streaming submodular maximization. However, it is not known whether the Ω(n/k²) lower bound used in these works is optimal for the problem, and in fact, it was conjectured by Cormode et al. that Ω(n) bits are necessary. We prove the optimal lower bound of Ω(n) for chain_{n,k} when k = o(n/log n) as our main result. This settles the open conjecture of Cormode et al., barring the range of k = Ω(n /log n). The main technique is a reduction to a non-standard index problem where the input to the players is such that the answer is biased away from uniform. This biased version of index is analyzed using tools from information theory. As a corollary, we get an improved lower bound for approximation of maximum independent set in vertex arrival streams via a reduction from chain directly.
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Janani Sundaresan. Optimal Communication Complexity of Chained Index. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 89:1-89:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sundaresan:LIPIcs.ITCS.2025.89,
  author =	{Sundaresan, Janani},
  title =	{{Optimal Communication Complexity of Chained Index}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{89:1--89:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.89},
  URN =		{urn:nbn:de:0030-drops-227172},
  doi =		{10.4230/LIPIcs.ITCS.2025.89},
  annote =	{Keywords: communication complexity, index communciation problem}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.47
Complexity Framework for Forbidden Subgraphs II: Edge Subdivision and the "H"-Graphs

Authors: Vadim Lozin, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Mark Siggers, Siani Smith, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
For a fixed set H of graphs, a graph G is H-subgraph-free if G does not contain any H ∈ H as a (not necessarily induced) subgraph. A recent framework gives a complete classification on H-subgraph-free graphs (for finite sets H) for problems that are solvable in polynomial time on graph classes of bounded treewidth, NP-complete on subcubic graphs, and whose NP-hardness is preserved under edge subdivision. While a lot of problems satisfy these conditions, there are also many problems that do not satisfy all three conditions and for which the complexity in H-subgraph-free graphs is unknown. We study problems for which only the first two conditions of the framework hold (they are solvable in polynomial time on classes of bounded treewidth and NP-complete on subcubic graphs, but NP-hardness is not preserved under edge subdivision). In particular, we make inroads into the classification of the complexity of four such problems: Hamilton Cycle, k-Induced Disjoint Paths, C₅-Colouring and Star 3-Colouring. Although we do not complete the classifications, we show that the boundary between polynomial time and NP-complete differs among our problems and also from problems that do satisfy all three conditions of the framework, in particular when we forbid certain subdivisions of the "H"-graph (the graph that looks like the letter "H"). Hence, we exhibit a rich complexity landscape among problems for H-subgraph-free graph classes.
Cite as

Vadim Lozin, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Mark Siggers, Siani Smith, and Erik Jan van Leeuwen. Complexity Framework for Forbidden Subgraphs II: Edge Subdivision and the "H"-Graphs. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 47:1-47:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lozin_et_al:LIPIcs.ISAAC.2024.47,
  author =	{Lozin, Vadim and Martin, Barnaby and Pandey, Sukanya and Paulusma, Dani\"{e}l and Siggers, Mark and Smith, Siani and van Leeuwen, Erik Jan},
  title =	{{Complexity Framework for Forbidden Subgraphs II: Edge Subdivision and the "H"-Graphs}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{47:1--47:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.47},
  URN =		{urn:nbn:de:0030-drops-221747},
  doi =		{10.4230/LIPIcs.ISAAC.2024.47},
  annote =	{Keywords: forbidden subgraph, complexity dichotomy, edge subdivision, treewidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.6
The Parameterised Complexity Of Integer Multicommodity Flow

Authors: Hans L. Bodlaender, Isja Mannens, Jelle J. Oostveen, Sukanya Pandey, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Path problem, have been considered. Therefore, we investigate the parameterised complexity of the general Integer Multicommodity Flow problem. We show that the decision version of this problem on directed graphs for a constant number of commodities, when the capacities are given in unary, is XNLP-complete with pathwidth as parameter and XALP-complete with treewidth as parameter. When the capacities are given in binary, the problem is NP-complete even for graphs of pathwidth at most 13. We give related results for undirected graphs. These results imply that the problem is unlikely to be fixed-parameter tractable by these parameters. In contrast, we show that the problem does become fixed-parameter tractable when weighted tree partition width (a variant of tree partition width for edge weighted graphs) is used as parameter.
Cite as

Hans L. Bodlaender, Isja Mannens, Jelle J. Oostveen, Sukanya Pandey, and Erik Jan van Leeuwen. The Parameterised Complexity Of Integer Multicommodity Flow. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2023.6,
  author =	{Bodlaender, Hans L. and Mannens, Isja and Oostveen, Jelle J. and Pandey, Sukanya and van Leeuwen, Erik Jan},
  title =	{{The Parameterised Complexity Of Integer Multicommodity Flow}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.6},
  URN =		{urn:nbn:de:0030-drops-194250},
  doi =		{10.4230/LIPIcs.IPEC.2023.6},
  annote =	{Keywords: multicommodity flow, parameterised complexity, XNLP-completeness, XALP-completeness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.57
Complexity Framework for Forbidden Subgraphs III: When Problems Are Tractable on Subcubic Graphs

Authors: Matthew Johnson, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Siani Smith, and Erik Jan van Leeuwen

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

Abstract
For any finite set ℋ = {H_1,…,H_p} of graphs, a graph is ℋ-subgraph-free if it does not contain any of H_1,…,H_p as a subgraph. In recent work, meta-classifications have been studied: these show that if graph problems satisfy certain prescribed conditions, their complexity can be classified on classes of ℋ-subgraph-free graphs. We continue this work and focus on problems that have polynomial-time solutions on classes that have bounded treewidth or maximum degree at most 3 and examine their complexity on H-subgraph-free graph classes where H is a connected graph. With this approach, we obtain comprehensive classifications for (Independent) Feedback Vertex Set, Connected Vertex Cover, Colouring and Matching Cut. This resolves a number of open problems. We highlight that, to establish that Independent Feedback Vertex Set belongs to this collection of problems, we first show that it can be solved in polynomial time on graphs of maximum degree 3. We demonstrate that, with the exception of the complete graph on four vertices, each graph in this class has a minimum size feedback vertex set that is also an independent set.
Cite as

Matthew Johnson, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Siani Smith, and Erik Jan van Leeuwen. Complexity Framework for Forbidden Subgraphs III: When Problems Are Tractable on Subcubic Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{johnson_et_al:LIPIcs.MFCS.2023.57,
  author =	{Johnson, Matthew and Martin, Barnaby and Pandey, Sukanya and Paulusma, Dani\"{e}l and Smith, Siani and van Leeuwen, Erik Jan},
  title =	{{Complexity Framework for Forbidden Subgraphs III: When Problems Are Tractable on Subcubic Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.57},
  URN =		{urn:nbn:de:0030-drops-185914},
  doi =		{10.4230/LIPIcs.MFCS.2023.57},
  annote =	{Keywords: forbidden subgraphs, independent feedback vertex set, treewidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.24
Parameterized Complexity of Streaming Diameter and Connectivity Problems

Authors: Jelle J. Oostveen and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size k allows for algorithms in the Adjacency List (AL) streaming model whose number of passes is constant and memory is 𝒪(log n) for any fixed k. Underlying these algorithms is a method to execute a breadth-first search in 𝒪(k) passes and 𝒪(k log n) bits of memory. On the negative end, we show that many other parameters lead to lower bounds in the AL model, where Ω(n/p) bits of memory is needed for any p-pass algorithm even for constant parameter values. In particular, this holds for graphs with a known modulator (deletion set) of constant size to a graph that has no induced subgraph isomorphic to a fixed graph H, for most H. For some cases, we can also show one-pass, Ω(n log n) bits of memory lower bounds. We also prove a much stronger Ω(n²/p) lower bound for Diameter on bipartite graphs. Finally, using the insights we developed into streaming parameterized graph exploration algorithms, we show a new streaming kernelization algorithm for computing a vertex cover of size k. This yields a kernel of 2k vertices (with 𝒪(k²) edges) produced as a stream in poly(k) passes and only 𝒪(k log n) bits of memory.
Cite as

Jelle J. Oostveen and Erik Jan van Leeuwen. Parameterized Complexity of Streaming Diameter and Connectivity Problems. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{oostveen_et_al:LIPIcs.IPEC.2022.24,
  author =	{Oostveen, Jelle J. and van Leeuwen, Erik Jan},
  title =	{{Parameterized Complexity of Streaming Diameter and Connectivity Problems}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.24},
  URN =		{urn:nbn:de:0030-drops-173808},
  doi =		{10.4230/LIPIcs.IPEC.2022.24},
  annote =	{Keywords: Stream, Streaming, Graphs, Parameter, Complexity, Diameter, Connectivity, Vertex Cover, Disjointness, Permutation}
}
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