19 Search Results for "Govind, R."

Document
DOI: 10.4230/LIPIcs.STACS.2026.12
Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density

Authors: Matthias Bentert, Tom-Lukas Breitkopf, Vincent Froese, Anton Herrmann, and André Nichterlein

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

Abstract
We study τ-Bounded-Density Edge Deletion (τ-BDED), where given an undirected graph G, the task is to remove as few edges as possible to obtain a graph G' where no subgraph of G' has density more than τ. The density of a (sub)graph is the number of edges divided by the number of vertices. This problem was recently introduced and shown to be NP-hard for τ ∈ {2/3, 3/4, 1 + 1/25}, but polynomial-time solvable for τ ∈ {0,1/2,1} [Bazgan et al., JCSS 2025]. We provide a complete dichotomy with respect to the target density τ: 1) If 2τ ∈ ℕ (half-integral target density) or τ < 2/3, then τ-BDED is polynomial-time solvable. 2) Otherwise, τ-BDED is NP-hard. We complement the NP-hardness with fixed-parameter tractability with respect to the treewidth of G. Moreover, for integral target density τ ∈ ℕ, we show τ-BDED to be solvable in randomized O(m^{1 + o(1)}) time. Our algorithmic results are based on a reduction to a new general flow problem on restricted networks that, depending on τ, can be solved via Maximum s-t-Flow or General Factors. We believe this connection between these variants of flow and matching to be of independent interest.
Cite as

Matthias Bentert, Tom-Lukas Breitkopf, Vincent Froese, Anton Herrmann, and André Nichterlein. Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2026.12,
  author =	{Bentert, Matthias and Breitkopf, Tom-Lukas and Froese, Vincent and Herrmann, Anton and Nichterlein, Andr\'{e}},
  title =	{{Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{12:1--12:20},
  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.2026.12},
  URN =		{urn:nbn:de:0030-drops-255012},
  doi =		{10.4230/LIPIcs.STACS.2026.12},
  annote =	{Keywords: Transshipment, Maximum Flow, General Factors, Matching, Graph Modification Problem}
}
Document
Research
DOI: 10.4230/TGDK.3.3.4
Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web

Authors: Florian Ruosch, Cristina Sarasua, and Abraham Bernstein

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract
In Argument Mining, predicting argumentative relations between texts (or spans) remains one of the most challenging aspects, even more so in the cross-document setting. This paper makes three key contributions to advance research in this domain. We first extend an existing dataset, the Sci-Arg corpus, by annotating it with explicit inter-document argumentative relations, thereby allowing arguments to be distributed over several documents forming an Argument Web; these new annotations are published using Semantic Web technologies (RDF, OWL). Second, we explore and evaluate three automated approaches for predicting these inter-document argumentative relations, establishing critical baselines on the new dataset. We find that a simple classifier based on discourse indicators with access to context outperforms neural methods. Third, we conduct a comparative analysis of these approaches for both intra- and inter-document settings, identifying statistically significant differences in results that indicate the necessity of distinguishing between these two scenarios. Our findings highlight significant challenges in this complex domain and open crucial avenues for future research on the Argument Web of Science, particularly for those interested in leveraging Semantic Web technologies and knowledge graphs to understand scholarly discourse. With this, we provide the first stepping stones in the form of a benchmark dataset, three baseline methods, and an initial analysis for a systematic exploration of this field relevant to the Web of Data and Science.
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Florian Ruosch, Cristina Sarasua, and Abraham Bernstein. Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 4:1-4:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ruosch_et_al:TGDK.3.3.4,
  author =	{Ruosch, Florian and Sarasua, Cristina and Bernstein, Abraham},
  title =	{{Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:33},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.4},
  URN =		{urn:nbn:de:0030-drops-252159},
  doi =		{10.4230/TGDK.3.3.4},
  annote =	{Keywords: Argument Mining, Large Language Models, Knowledge Graphs, Link Prediction}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.3
Generalized Graph Packing Problems Parameterized by Treewidth

Authors: Barış Can Esmer and Dániel Marx

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
H-Packing is the problem of finding a maximum number of vertex-disjoint copies of H in a given graph G. H-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of G exactly once. Our goal is to study these problems and some generalizations on bounded-treewidth graphs. The case of H being a triangle is well understood: given a tree decomposition of G having treewidth tw, the K₃-Packing problem can be solved in time 2^tw⋅ n^O(1), while Lokshtanov et al. [ACM Transactions on Algorithms 2018] showed, under the Strong Exponential-Time Hypothesis (SETH), that there is no (2-ε)^tw⋅ n^O(1) algorithm for any ε > 0 even for K₃-Partition. Similar results can be obtained for any other clique K_d for d ≥ 3. We provide generalizations in two directions: - We consider a generalization of the problem where every vertex can be used at most c times for some c ≥ 1. When H is any clique K_d with d ≥ 3, then we give upper and lower bounds showing that the optimal running time increases to (c+1)^tw⋅ n^O(1). We consider two variants depending on whether a copy of H can be used multiple times in the packing. - If H is not a clique, then the dependence of the running time on treewidth may not be even single exponential. Specifically, we show that if H is any fixed graph where not every 2-connected component is a clique, then there is no 2^o(tw log tw)⋅ n^O(1) algorithm for H-Partition, assuming the Exponential-Time Hypothesis (ETH).
Cite as

Barış Can Esmer and Dániel Marx. Generalized Graph Packing Problems Parameterized by Treewidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canesmer_et_al:LIPIcs.ESA.2025.3,
  author =	{Can Esmer, Bar{\i}\c{s} and Marx, D\'{a}niel},
  title =	{{Generalized Graph Packing Problems Parameterized by Treewidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.3},
  URN =		{urn:nbn:de:0030-drops-244713},
  doi =		{10.4230/LIPIcs.ESA.2025.3},
  annote =	{Keywords: Graph Packing, Graph Partitioning, Parameterized Complexity, Treewidth, Pathwidth, pw-SETH, Single-Exponential Lower Bound, Slightly Superexponential Lower Bound}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.13
Tight Bounds for Some Classical Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, and Stefan Kratsch

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Cutwidth is a widely studied parameter and it quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth upper-bounds pathwidth. The SETH-tight parameterized complexity of problems on graphs of bounded pathwidth (and treewidth) has been actively studied over the past decade while for cutwidth the complexity of many classical problems remained open. For Hamiltonian Cycle, it is known that a (2+√2)^{pw} n^𝒪(1) algorithm is optimal for pathwidth under SETH [Cygan et al. JACM 2018]. Van Geffen et al. [J. Graph Algorithms Appl. 2020] and Bojikian et al. [STACS 2023] asked which running time is optimal for this problem parameterized by cutwidth. We answer this question with (1+√2)^{ctw} n^𝒪(1) by providing matching upper and lower bounds. Second, as our main technical contribution, we close the gap left by van Heck [2018] for Partition Into Triangles (and Triangle Packing) by improving both upper and lower bound and getting a tight bound of ∛{3}^{ctw} n^𝒪(1), which to our knowledge exhibits the only known tight non-integral basis apart from Hamiltonian Cycle [Cygan et al. JACM 2018] and C₄-Hitting Set [SODA 2025]. We show that the cuts inducing a disjoint union of paths of length three (unions of so-called Z-cuts) lie at the core of the complexity of the problem - usually lower-bound constructions use simpler cuts inducing either a matching or a disjoint union of bicliques. Finally, we determine the optimal running times for Max Cut (2^{ctw} n^𝒪(1)) and Induced Matching (3^{ctw} n^𝒪(1)) by providing matching lower bounds for the existing algorithms - the latter result also answers an open question for treewidth by Chaudhary and Zehavi [WG 2023].
Cite as

Narek Bojikian, Vera Chekan, and Stefan Kratsch. Tight Bounds for Some Classical Problems Parameterized by Cutwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.ESA.2025.13,
  author =	{Bojikian, Narek and Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Bounds for Some Classical Problems Parameterized by Cutwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.13},
  URN =		{urn:nbn:de:0030-drops-244815},
  doi =		{10.4230/LIPIcs.ESA.2025.13},
  annote =	{Keywords: Parameterized complexity, cutwidth, Hamiltonian cycle, triangle packing, max cut, induced matching}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.1
Amortized Locally Decodable Codes for Insertions and Deletions

Authors: Jeremiah Blocki and Justin Zhang

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
Locally Decodable Codes (LDCs) are error correcting codes which permit the recovery of any single message symbol with a low number of queries to the codeword (the locality). Traditional LDC tradeoffs between the rate, locality, and error tolerance are undesirable even in relaxed settings where the encoder/decoder share randomness or where the channel is resource-bounded. Recent work by Blocki and Zhang initiated the study of Hamming amortized Locally Decodable Codes (aLDCs), which allow the local decoder to amortize their number of queries over the recovery of a small subset of message symbols. Surprisingly, Blocki and Zhang construct asymptotically ideal (constant rate, constant amortized locality, and constant error tolerance) Hamming aLDCs in private-key and resource-bounded settings. While this result overcame previous barriers and impossibility results for Hamming LDCs, it is not clear whether the techniques extend to Insdel LDCs. Constructing Insdel LDCs which are resilient to insertion and/or deletion errors is known to be even more challenging. For example, Gupta (STOC'24) proved that no Insdel LDC with constant rate and error tolerance exists even in relaxed settings. Our first contribution is to provide a Hamming-to-Insdel compiler which transforms any amortized Hamming LDC that satisfies a particular property (consecutive interval querying) to amortized Insdel LDC while asymptotically preserving the rate, error tolerance and amortized locality. Prior Hamming-to-Insdel compilers of Ostrovsky and Paskin-Cherniavsky (ICITS'15) and Block et al. (FSTTCS'20) worked for arbitrary Hamming LDCs, but incurred an undesirable polylogarithmic blow-up in the locality. Our second contribution is a construction of an ideal amortized Hamming LDC which satisfies our special property (consecutive interval querying) in the relaxed settings where the sender/receiver share randomness or where the channel is resource bounded. Taken together, we obtain ideal Insdel aLDCs in private-key and resource-bounded settings with constant amortized locality, constant rate and constant error tolerance. This result is surprising in light of Gupta’s (STOC'24) impossibility result which demonstrates a strong separation between locality and amortized locality for Insdel LDCs.
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Jeremiah Blocki and Justin Zhang. Amortized Locally Decodable Codes for Insertions and Deletions. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blocki_et_al:LIPIcs.ITC.2025.1,
  author =	{Blocki, Jeremiah and Zhang, Justin},
  title =	{{Amortized Locally Decodable Codes for Insertions and Deletions}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{1:1--1:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.1},
  URN =		{urn:nbn:de:0030-drops-243518},
  doi =		{10.4230/LIPIcs.ITC.2025.1},
  annote =	{Keywords: Amortized Locally Decodable Codes, Insertion and Deletion Errors}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.22
Partial-Order Reduction Is Hard

Authors: Frédéric Herbreteau, Sarah Larroze-Jardiné, and Igor Walukiewicz

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
The goal of partial-order methods is to accelerate the exploration of concurrent systems by examining only a representative subset of all possible runs. The stateful approach builds a transition system with representative runs, while the stateless method simply enumerates them. The stateless approach may be preferable if the transition system is tree-like; otherwise, the stateful method is more effective. In the last decade, optimality has been a guiding principle for developing stateless partial-order reduction algorithms, and without doubt contributed to big progress in the field. In this paper we ask if we can get a similar principle for the stateful approach. We show that in stateful exploration, a polynomially close to optimal partial-order algorithm cannot exist unless P=NP. The result holds even for acyclic programs with just await instructions. This lower bound result justifies systematic study of heuristics for stateful partial-order reduction. We propose a notion of IFS oracle as a useful abstraction. The oracle can be used to get a very simple optimal stateless algorithm, which can then be adapted to a non-optimal stateful algorithm. While in general the oracle problem is NP-hard, we show a simple case where it can be solved in linear time.
Cite as

Frédéric Herbreteau, Sarah Larroze-Jardiné, and Igor Walukiewicz. Partial-Order Reduction Is Hard. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{herbreteau_et_al:LIPIcs.CONCUR.2025.22,
  author =	{Herbreteau, Fr\'{e}d\'{e}ric and Larroze-Jardin\'{e}, Sarah and Walukiewicz, Igor},
  title =	{{Partial-Order Reduction Is Hard}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.22},
  URN =		{urn:nbn:de:0030-drops-239727},
  doi =		{10.4230/LIPIcs.CONCUR.2025.22},
  annote =	{Keywords: Formal verification, Concurrent systems, Partial-order reduction, Complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.7
Parameterised Holant Problems

Authors: Panagiotis Aivasiliotis, Andreas Göbel, Marc Roth, and Johannes Schmitt

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

Abstract
We investigate the complexity of parameterised holant problems p-Holant(𝒮) for families of symmetric signatures 𝒮. The parameterised holant framework has been introduced by Curticapean in 2015 as a counter-part to the classical and well-established theory of holographic reductions and algorithms, and it constitutes an extensive family of coloured and weighted counting constraint satisfaction problems on graph-like structures, encoding as special cases various well-studied counting problems in parameterised and fine-grained complexity theory such as counting edge-colourful k-matchings, graph-factors, Eulerian orientations or, more generally, subgraphs with weighted degree constraints. We establish an exhaustive complexity trichotomy along the set of signatures 𝒮: Depending on the signatures, p-Holant(𝒮) is either 1) solvable in "FPT-near-linear time", i.e., in time f(k)⋅ 𝒪̃(|x|), or 2) solvable in "FPT-matrix-multiplication time", i.e., in time f(k)⋅ {𝒪}(n^{ω}), where n is the number of vertices of the underlying graph, but not solvable in FPT-near-linear time, unless the Triangle Conjecture fails, or 3) #W[1]-complete and no significant improvement over the naive brute force algorithm is possible unless the Exponential Time Hypothesis fails. This classification reveals a significant and surprising gap in the complexity landscape of parameterised Holants: Not only is every instance either fixed-parameter tractable or #W[1]-complete, but additionally, every FPT instance is solvable in time (at most) f(k)⋅ {𝒪}(n^{ω}). We show that there are infinitely many instances of each of the types; for example, all constant signatures yield holant problems of type (1), and the problem of counting edge-colourful k-matchings modulo p is of type (p) for p ∈ {2,3}. Finally, we also establish a complete classification for a natural uncoloured version of parameterised holant problem p-UnColHolant(𝒮), which encodes as special cases the non-coloured analogues of the aforementioned examples. We show that the complexity of p-UnColHolant(𝒮) is different: Depending on 𝒮 all instances are either solvable in FPT-near-linear time, or #W[1]-complete, that is, there are no instances of type (2).
Cite as

Panagiotis Aivasiliotis, Andreas Göbel, Marc Roth, and Johannes Schmitt. Parameterised Holant Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aivasiliotis_et_al:LIPIcs.ICALP.2025.7,
  author =	{Aivasiliotis, Panagiotis and G\"{o}bel, Andreas and Roth, Marc and Schmitt, Johannes},
  title =	{{Parameterised Holant Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{7:1--7:14},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-233842},
  doi =		{10.4230/LIPIcs.ICALP.2025.7},
  annote =	{Keywords: holant problems, counting problems, parameterised algorithms, fine-grained complexity theory, homomorphisms}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.20
Group Fairness and Multi-Criteria Optimization in School Assignment

Authors: Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We consider the problem of assigning students to schools when students have different utilities for schools and schools have limited capacities. The students belong to demographic groups, and fairness over these groups is captured either by concave objectives, or additional constraints on the utility of the groups. We present approximation algorithms for this assignment problem with group fairness via convex program rounding. These algorithms achieve various trade-offs between capacity violation and running time. We also show that our techniques easily extend to the setting where there are arbitrary constraints on the feasible assignment, capturing multi-criteria optimization. We present simulation results that demonstrate that the rounding methods are practical even on large problem instances, with the empirical capacity violation being much better than the theoretical bounds.
Cite as

Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar. Group Fairness and Multi-Criteria Optimization in School Assignment. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{k.a._et_al:LIPIcs.FORC.2025.20,
  author =	{K. A., Santhini and Munagala, Kamesh and Nasre, Meghana and S. Sankar, Govind},
  title =	{{Group Fairness and Multi-Criteria Optimization in School Assignment}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.20},
  URN =		{urn:nbn:de:0030-drops-231471},
  doi =		{10.4230/LIPIcs.FORC.2025.20},
  annote =	{Keywords: School Assignment, Approximation Algorithms, Group Fairness}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.41
Residue Domination in Bounded-Treewidth Graphs

Authors: Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
For the vertex selection problem (σ,ρ)-DomSet one is given two fixed sets σ and ρ of integers and the task is to decide whether we can select vertices of the input graph such that, for every selected vertex, the number of selected neighbors is in σ and, for every unselected vertex, the number of selected neighbors is in ρ [Telle, Nord. J. Comp. 1994]. This framework covers many fundamental graph problems such as Independent Set and Dominating Set. We significantly extend the recent result by Focke et al. [SODA 2023] to investigate the case when σ and ρ are two (potentially different) residue classes modulo m ≥ 2. We study the problem parameterized by treewidth and present an algorithm that solves in time m^tw ⋅ n^O(1) the decision, minimization and maximization version of the problem. This significantly improves upon the known algorithms where for the case m ≥ 3 not even an explicit running time is known. We complement our algorithm by providing matching lower bounds which state that there is no (m-ε)^pw ⋅ n^O(1)-time algorithm parameterized by pathwidth pw, unless SETH fails. For m = 2, we extend these bounds to the minimization version as the decision version is efficiently solvable.
Cite as

Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz. Residue Domination in Bounded-Treewidth Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{greilhuber_et_al:LIPIcs.STACS.2025.41,
  author =	{Greilhuber, Jakob and Schepper, Philipp and Wellnitz, Philip},
  title =	{{Residue Domination in Bounded-Treewidth Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{41:1--41:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.41},
  URN =		{urn:nbn:de:0030-drops-228675},
  doi =		{10.4230/LIPIcs.STACS.2025.41},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Generalized Dominating Set, Strong Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.5
MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm

Authors: S. Akshay, Paul Gastin, R. Govind, and B. Srivathsan

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
The translation of Metric Interval Temporal Logic (MITL) to timed automata is a topic that has been extensively studied. A key challenge here is the conversion of future modalities into equivalent automata. Typical conversions equip the automata with a guess-and-check mechanism to ascertain the truth of future modalities. Guess-and-check can be naturally implemented via alternation. However, since timed automata tools do not handle alternation, existing methods perform an additional step of converting the alternating timed automata into timed automata. This "de-alternation" step proceeds by an intricate finite abstraction of the space of configurations of the alternating automaton. Recently, a model of generalized timed automata (GTA) has been proposed. The model comes with several powerful additional features, and yet, the best known zone-based reachability algorithms for timed automata have been extended to the GTA model, with the same complexity for all the zone operations. An attractive feature of GTAs is the presence of future clocks which act like timers that guess a time to an event and stay alive until a timeout. Future clocks seem to provide another natural way to implement the guess-and-check: start the future clock with a guessed time to an event and check its occurrence using a timeout. Indeed, using this feature, we provide a new concise translation from MITL to GTA. In particular, for the timed until modality, our translation offers an exponential improvement w.r.t. the state-of-the-art. Thanks to this conversion, MITL model checking reduces to checking liveness for GTAs. However, no liveness algorithm is known for GTAs. Due to the presence of future clocks, there is no finite time-abstract bisimulation (region equivalence) for GTAs, whereas liveness algorithms for timed automata crucially rely on the presence of the finite region equivalence. As our second contribution, we provide a new zone-based algorithm for checking Büchi non-emptiness in GTAs, which circumvents this fundamental challenge.
Cite as

S. Akshay, Paul Gastin, R. Govind, and B. Srivathsan. MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2024.5,
  author =	{Akshay, S. and Gastin, Paul and Govind, R. and Srivathsan, B.},
  title =	{{MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.5},
  URN =		{urn:nbn:de:0030-drops-207774},
  doi =		{10.4230/LIPIcs.CONCUR.2024.5},
  annote =	{Keywords: MITL model checking, timed automata, zones, liveness}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.21
Reversible Transducers over Infinite Words

Authors: Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to synthesis, where transformation specifications are converted into equivalent transducers. These specifications are presented in a modular way, and composing the resultant machines simulates the full specification. An important result by Dartois et al. [Luc Dartois et al., 2017] shows that composition of two-way transducers enjoy a polynomial composition when the underlying transducer is reversible, that is, if they are both deterministic and co-deterministic. This is a major improvement over general deterministic two-way transducers, for which composition causes a doubly exponential blow-up in the size of the inputs in general. Moreover, they show that reversible two-way transducers have the same expressiveness as deterministic two-way transducers. However, the notion of reversible two-way transducers over infinite words as well as the question of their expressiveness were not studied yet. In this article, we introduce the class of reversible two-way transducers over infinite words and show that they enjoy the same expressive power as deterministic two-way transducers over infinite words. This is done through a non-trivial, effective construction inducing a single exponential blow-up in the set of states. Further, we also prove that composing two reversible two-way transducers over infinite words incurs only a polynomial complexity, thereby providing an efficient procedure for composition of transducers over infinite words.
Cite as

Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna. Reversible Transducers over Infinite Words. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dartois_et_al:LIPIcs.CONCUR.2024.21,
  author =	{Dartois, Luc and Gastin, Paul and Germerie Guizouarn, Lo\"{i}c and Govind, R. and Krishna, Shankaranarayanan},
  title =	{{Reversible Transducers over Infinite Words}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.21},
  URN =		{urn:nbn:de:0030-drops-207932},
  doi =		{10.4230/LIPIcs.CONCUR.2024.21},
  annote =	{Keywords: Transducers, Regular functions, Reversibility, Composition, SSTs}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.2
Probabilistic Metric Embedding via Metric Labeling

Authors: Kamesh Munagala, Govind S. Sankar, and Erin Taylor

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

Abstract
We consider probabilistic embedding of metric spaces into ultra-metrics (or equivalently to a constant factor, into hierarchically separated trees) to minimize the expected distortion of any pairwise distance. Such embeddings have been widely used in network design and online algorithms. Our main result is a polynomial time algorithm that approximates the optimal distortion on any instance to within a constant factor. We achieve this via a novel LP formulation that reduces this problem to a probabilistic version of uniform metric labeling.
Cite as

Kamesh Munagala, Govind S. Sankar, and Erin Taylor. Probabilistic Metric Embedding via Metric Labeling. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{munagala_et_al:LIPIcs.APPROX/RANDOM.2023.2,
  author =	{Munagala, Kamesh and Sankar, Govind S. and Taylor, Erin},
  title =	{{Probabilistic Metric Embedding via Metric Labeling}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{2:1--2:10},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.2},
  URN =		{urn:nbn:de:0030-drops-188279},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.2},
  annote =	{Keywords: Metric Embedding, Approximation Algorithms, Ultrametrics}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.22
Anti-Factor Is FPT Parameterized by Treewidth and List Size (But Counting Is Hard)

Authors: Dániel Marx, Govind S. Sankar, and Philipp Schepper

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

Abstract
In the general AntiFactor problem, a graph G and, for every vertex v of G, a set X_v ⊆ ℕ of forbidden degrees is given. The task is to find a set S of edges such that the degree of v in S is not in the set X_v. Standard techniques (dynamic programming plus fast convolution) can be used to show that if M is the largest forbidden degree, then the problem can be solved in time (M+2)^{tw}⋅n^{O(1)} if a tree decomposition of width tw is given. However, significantly faster algorithms are possible if the sets X_v are sparse: our main algorithmic result shows that if every vertex has at most x forbidden degrees (we call this special case AntiFactor_x), then the problem can be solved in time (x+1)^{O(tw)}⋅n^{O(1)}. That is, AntiFactor_x is fixed-parameter tractable parameterized by treewidth tw and the maximum number x of excluded degrees. Our algorithm uses the technique of representative sets, which can be generalized to the optimization version, but (as expected) not to the counting version of the problem. In fact, we show that #AntiFactor₁ is already #W[1]-hard parameterized by the width of the given decomposition. Moreover, we show that, unlike for the decision version, the standard dynamic programming algorithm is essentially optimal for the counting version. Formally, for a fixed nonempty set X, we denote by X-AntiFactor the special case where every vertex v has the same set X_v = X of forbidden degrees. We show the following lower bound for every fixed set X: if there is an ε > 0 such that #X-AntiFactor can be solved in time (max X+2-ε)^{tw}⋅n^{O(1)} given a tree decomposition of width tw, then the Counting Strong Exponential-Time Hypothesis (#SETH) fails.
Cite as

Dániel Marx, Govind S. Sankar, and Philipp Schepper. Anti-Factor Is FPT Parameterized by Treewidth and List Size (But Counting Is Hard). In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 22:1-22:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{marx_et_al:LIPIcs.IPEC.2022.22,
  author =	{Marx, D\'{a}niel and Sankar, Govind S. and Schepper, Philipp},
  title =	{{Anti-Factor Is FPT Parameterized by Treewidth and List Size (But Counting Is Hard)}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{22:1--22:23},
  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.2022.22},
  URN =		{urn:nbn:de:0030-drops-173780},
  doi =		{10.4230/LIPIcs.IPEC.2022.22},
  annote =	{Keywords: Anti-Factor, General Factor, Treewidth, Representative Sets, SETH}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.13
Simulations for Event-Clock Automata

Authors: S. Akshay, Paul Gastin, R. Govind, and B. Srivathsan

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
Event-clock automata are a well-known subclass of timed automata which enjoy admirable theoretical properties, e.g., determinizability, and are practically useful to capture timed specifications. However, unlike for timed automata, there exist no implementations for event-clock automata. A main reason for this is the difficulty in adapting zone-based algorithms, critical in the timed automata setting, to the event-clock automata setting. This difficulty was studied in [Gilles Geeraerts et al., 2011; Gilles Geeraerts et al., 2014], where the authors also proposed a solution using zone extrapolations. In this paper, we propose an alternative zone-based algorithm, using simulations for finiteness, to solve the reachability problem for event-clock automata. Our algorithm exploits the 𝒢-simulation framework, which is the coarsest known simulation relation for reachability, and has been recently used for advances in other extensions of timed automata.
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S. Akshay, Paul Gastin, R. Govind, and B. Srivathsan. Simulations for Event-Clock Automata. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2022.13,
  author =	{Akshay, S. and Gastin, Paul and Govind, R. and Srivathsan, B.},
  title =	{{Simulations for Event-Clock Automata}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.13},
  URN =		{urn:nbn:de:0030-drops-170766},
  doi =		{10.4230/LIPIcs.CONCUR.2022.13},
  annote =	{Keywords: Event-clock automata, verification, zones, simulations, reachability}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.95
Degrees and Gaps: Tight Complexity Results of General Factor Problems Parameterized by Treewidth and Cutwidth

Authors: Dániel Marx, Govind S. Sankar, and Philipp Schepper

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In the General Factor problem, we are given an undirected graph G and for each vertex v ∈ V(G) a finite set B_v of non-negative integers. The task is to decide if there is a subset S ⊆ E(G) such that deg_S(v) ∈ B_v for all vertices v of G. Define the max-gap of a finite integer set B to be the largest d ≥ 0 such that there is an a ≥ 0 with [a,a+d+1] ∩ B = {a,a+d+1}. Cornuéjols showed in 1988 that if the max-gap of all sets B_v is at most 1, then the decision version of General Factor is polynomial-time solvable. This result was extended 2018 by Dudycz and Paluch for the optimization (i.e. minimization and maximization) versions. We present a general algorithm counting the number of solutions of a certain size in time #2 (M+1)^{tw}^{𝒪(1)}, given a tree decomposition of width tw, where M is the maximum integer over all B_v. By using convolution techniques from van Rooij (2020), we improve upon the previous (M+1)^{3tw}^𝒪(1) time algorithm by Arulselvan et al. from 2018. We prove that this algorithm is essentially optimal for all cases that are not trivial or polynomial time solvable for the decision, minimization or maximization versions. Our lower bounds show that such an improvement is not even possible for B-Factor, which is General Factor on graphs where all sets B_v agree with the fixed set B. We show that for every fixed B where the problem is NP-hard, our (max B+1)^tw^𝒪(1) algorithm cannot be significantly improved: assuming the Strong Exponential Time Hypothesis (SETH), no algorithm can solve B-Factor in time (max B+1-ε)^tw^𝒪(1) for any ε > 0. We extend this bound to the counting version of B-Factor for arbitrary, non-trivial sets B, assuming #SETH. We also investigate the parameterization of the problem by cutwidth. Unlike for treewidth, having a larger set B does not appear to make the problem harder: we give a 2^cutw^𝒪(1) algorithm for any B and provide a matching lower bound that this is optimal for the NP-hard cases.
Cite as

Dániel Marx, Govind S. Sankar, and Philipp Schepper. Degrees and Gaps: Tight Complexity Results of General Factor Problems Parameterized by Treewidth and Cutwidth. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{marx_et_al:LIPIcs.ICALP.2021.95,
  author =	{Marx, D\'{a}niel and Sankar, Govind S. and Schepper, Philipp},
  title =	{{Degrees and Gaps: Tight Complexity Results of General Factor Problems Parameterized by Treewidth and Cutwidth}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{95:1--95:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.95},
  URN =		{urn:nbn:de:0030-drops-141647},
  doi =		{10.4230/LIPIcs.ICALP.2021.95},
  annote =	{Keywords: General Factor, General Matching, Treewidth, Cutwidth}
}
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