52 Search Results for "Walsh, Toby"

Document
DOI: 10.4230/LIPIcs.CPM.2026.12
Maximizing Diversity in (Near-)Median String Selection

Authors: Diptarka Chakraborty, Rudrayan Kundu, Nidhi Purohit, and Aravinda Kanchana Ruwanpathirana

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

Abstract
Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the underlying metric, this problem has extensive applications, ranging from bioinformatics to pattern recognition. However, modern applications often require the generation of multiple (near-)optimal yet diverse median strings to enhance flexibility and robustness in decision-making. In this study, we address this need by focusing on two prominent diversity measures: sum dispersion and min dispersion. We first introduce an exact algorithm for the diameter variant of the problem, which identifies pairs of near-optimal medians that are maximally diverse. Subsequently, we propose a (1-ε)-approximation algorithm (for any ε > 0) for sum dispersion, as well as a bi-criteria approximation algorithm for the more challenging min dispersion case, allowing the generation of multiple (more than two) diverse near-optimal Hamming medians. Our approach primarily leverages structural insights into the Hamming median space and also draws on techniques from error-correcting code construction to establish these results.
Cite as

Diptarka Chakraborty, Rudrayan Kundu, Nidhi Purohit, and Aravinda Kanchana Ruwanpathirana. Maximizing Diversity in (Near-)Median String Selection. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chakraborty_et_al:LIPIcs.CPM.2026.12,
  author =	{Chakraborty, Diptarka and Kundu, Rudrayan and Purohit, Nidhi and Ruwanpathirana, Aravinda Kanchana},
  title =	{{Maximizing Diversity in (Near-)Median String Selection}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{12:1--12:15},
  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.2026.12},
  URN =		{urn:nbn:de:0030-drops-259382},
  doi =		{10.4230/LIPIcs.CPM.2026.12},
  annote =	{Keywords: Diversity maximization, Hamming median, diameter, dispersion, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.26
On the Parameterized Complexity of Min-Sum-Radii

Authors: Pankaj Kumar, Haiko Müller, Sebastian Ordyniak, and Melanie Schmidt

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

Abstract
In the Min-Sum-Radii (MSR) clustering problem, we are given a finite set X of n points in a metric space. The objective is to find at most k clusters centered at a subset of these points such that every point of X is assigned to one of the clusters, minimizing the sum of the radii of the clusters. The problem is known to be NP-hard even on metrics induced by weighted planar graphs and metrics with constant doubling dimension, as shown by Gibson et al. (SWAT 2008). In this work, we investigate the parameterized complexity of MSR on metrics induced by undirected graphs. We distinguish between weighted graph metrics (with positive edge weights) and unweighted graph metrics (where all edges have unit weight). Weighted Graph Metrics. We show that MSR is W[1]-hard on metrics induced by weighted bipartite graphs, when parameterized by the combined parameter k the number of clusters and Δ the cost of the clustering. We then investigate the structural parameterized complexity of the problem. Drexler et al. [doi:10.48550/arXiv.2310.02130] showed that the MSR problem admits an XP algorithm on metrics induced by weighted graphs when parameterized by treewidth, and asked whether this can be improved to fixed-parameter tractability. We first answer their question in the negative, and more strongly show that MSR stays W[1]-hard on metrics induced by undirected weighted bipartite graphs when parameterized by the vertex cover number plus k. We then turn our attention to parameters for dense graphs and show that MSR remains W[1]-hard when parameterized by k+Δ even on cliques and complete bipartite graphs. On the positive side, we employ the known XP algorithm parameterized by treewidth, to show that the MSR problem is FPT when parameterized by the parameter treewidth plus Δ. Together, these results provide a complete picture of the parameterized complexity of MSR with respect to any combination of parameters k, Δ, as well as structural parameters for sparse graphs above vertex cover and known parameters for dense graphs (such as neighborhood diversity and modular width). Unweighted Graph Metrics. The story is rather different for unweighted graphs, since it is a long standing open question whether MSR on metrics induced by undirected graphs is solvable in polynomial-time. Although we cannot answer this question, we provide classical and parameterized hardness results for two very closely related problems, namely Exact-MSR (MSR and one wants to find exactly k clusters) and Allowed-Centers-MSR (MSR with an additional set of allowed cluster centers). We also show that MSR as well as these two problems are fixed-parameter tractable parameterized by the treedepth of the input graph.
Cite as

Pankaj Kumar, Haiko Müller, Sebastian Ordyniak, and Melanie Schmidt. On the Parameterized Complexity of Min-Sum-Radii. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kumar_et_al:LIPIcs.SWAT.2026.26,
  author =	{Kumar, Pankaj and M\"{u}ller, Haiko and Ordyniak, Sebastian and Schmidt, Melanie},
  title =	{{On the Parameterized Complexity of Min-Sum-Radii}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{26:1--26:18},
  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.2026.26},
  URN =		{urn:nbn:de:0030-drops-260623},
  doi =		{10.4230/LIPIcs.SWAT.2026.26},
  annote =	{Keywords: Parameterized complexity, Min-Sum-Radii clustering}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.38
Fairness and Efficiency in Two-Sided Matching Markets

Authors: Pallavi Jain, Palash Jha, and Shubham Solanki

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We propose a new fairness notion, motivated by the practical challenge of allocating teaching assistants (TAs) to courses in a department. Each course requires a certain number of TAs and each TA has preferences over the courses they want to assist. Similarly, each course instructor has preferences over the TAs who applied for their course. We demand fairness and efficiency for both sides separately, giving rise to the following criteria: (i) every course gets the required number of TAs and the average utility of the assigned TAs meets a threshold; (ii) the allocation of courses to TAs is envy-free, where a TA envies another TA if the former prefers the latter’s course and has a higher or equal grade in that course. Note that the definition of envy-freeness here differs from the one in the literature, and we call it merit-based envy-freeness. We show that the problem of finding a merit-based envy-free and efficient matching is NP-hard even for very restricted settings, such as two courses and uniform valuations; constant degree, constant capacity of TAs for every course, valuations in the range {0,1,2,3}, identical valuations from TAs, and even more. To find tractable results, we consider some restricted instances, such as, strict valuation of TAs for courses, the difference between the number of positively valued TAs for a course and the capacity, the number of positively valued TAs/courses, types of valuation functions, and obtained some polynomial-time solvable cases, showing the contrast with intractable results. We further studied the problem in the paradigm of parameterized algorithms and designed some exact and approximation algorithms.
Cite as

Pallavi Jain, Palash Jha, and Shubham Solanki. Fairness and Efficiency in Two-Sided Matching Markets. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jain_et_al:LIPIcs.FSTTCS.2025.38,
  author =	{Jain, Pallavi and Jha, Palash and Solanki, Shubham},
  title =	{{Fairness and Efficiency in Two-Sided Matching Markets}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.38},
  URN =		{urn:nbn:de:0030-drops-251186},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.38},
  annote =	{Keywords: Fair Matching, Envy-Freeness, Efficiency}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.29
Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division

Authors: Ajaykrishnan E S and Daniel Lokshtanov

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent’s share. Focusing on agents with additive valuations, we show that the problem remains computationally hard when parameterized by p and the number of agents. This result holds even for star graphs and with the input numbers given in unary representation, thereby resolving an open problem posed by Gahlawat and Zehavi (FSTTCS 2023). In stark contrast, we show that if one is willing to tolerate even the slightest amount of envy, then the problem becomes efficient with respect to the natural parameters. Specifically, we design an Efficient Parameterized Approximation Scheme parameterized by p and the number of agent types. Our algorithm works on general graphs and remains efficient even when the input numbers are provided in binary representation.
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Ajaykrishnan E S and Daniel Lokshtanov. Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{es_et_al:LIPIcs.FSTTCS.2025.29,
  author =	{E S, Ajaykrishnan and Lokshtanov, Daniel},
  title =	{{Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.29},
  URN =		{urn:nbn:de:0030-drops-251101},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.29},
  annote =	{Keywords: Envy-Free Incomplete Connected Fair Division, Efficient Parameterized Approximation Scheme, W\lbrack1\rbrack-hardness}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.25
On the Interplay of Cube Learning and Dependency Schemes in {QCDCL} Proof Systems

Authors: Abhimanyu Choudhury and Meena Mahajan

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Quantified Conflict Driven Clause Leaning (QCDCL) is one of the main approaches to solving Quantified Boolean Formulas (QBF). Cube-learning is employed in this approach to ensure that true formulas can be verified. Dependency Schemes help to detect spurious dependencies that are implied by the variable ordering in the quantifier prefix of QBFs but are not essential for constructing (counter)models. This detection can provably shorten refutations in specific proof systems, and is expected to speed up runs of QBF solvers. The simplest underlying proof system [BeyersdorffBöhm-LMCS2023], formalises the reasoning in the QCDCL approach on false formulas, when neither cube-learning nor dependency schemes is used. The work of [BöhmPeitlBeyersdorff-AI2024] further incorporates cube-learning. The work of [ChoudhuryMahajan-JAR2024] incorporates a limited use of dependency schemes, but without cube-learning. In this work, proof systems underlying the reasoning of QCDCL solvers which use cube learning, and which use dependency schemes at all stages, are formalised. Sufficient conditions for soundness and completeness are presented, and it is shown that using the standard and reflexive resolution path dependency schemes (𝙳^{std} and 𝙳^{rrs}) to relax the decision order provably shortens refutations. When the decisions are restricted to follow quantification order, but dependency schemes are used in propagation and learning, in conjunction with cube-learning, the resulting proof systems using the dependency schemes 𝙳^{std} and 𝙳^{rrs} are investigated in detail and their relative strengths are analysed.
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Abhimanyu Choudhury and Meena Mahajan. On the Interplay of Cube Learning and Dependency Schemes in {QCDCL} Proof Systems. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{choudhury_et_al:LIPIcs.FSTTCS.2025.25,
  author =	{Choudhury, Abhimanyu and Mahajan, Meena},
  title =	{{On the Interplay of Cube Learning and Dependency Schemes in \{QCDCL\} Proof Systems}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.25},
  URN =		{urn:nbn:de:0030-drops-251062},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.25},
  annote =	{Keywords: QBF, CDCL, Resolution, Dependency schemes}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.32
Fair Rent Division: New Budget and Rent Constraints

Authors: Rohith Reddy Gangam, Shayan Taherijam, and Vijay V. Vazirani

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the classical rent division problem, where n agents must allocate n indivisible rooms and split a fixed total rent R. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent’s room and rent to their own. This problem has been extensively studied under standard assumptions, where efficient algorithms for computing EF allocations are known. We extend this framework by introducing two practically motivated constraints: (i) lower and upper bounds on room rents, and (ii) room-specific budget for agents. We develop efficient combinatorial algorithms that either compute a feasible EF allocation or certify infeasibility. We further design algorithms to optimize over EF allocations using natural fairness objectives such as maximin utility, leximin utility, and minimum utility spread. Our approach unifies both constraint types within a single algorithmic framework, advancing the applicability of fair division methods in real-world platforms such as Spliddit.
Cite as

Rohith Reddy Gangam, Shayan Taherijam, and Vijay V. Vazirani. Fair Rent Division: New Budget and Rent Constraints. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gangam_et_al:LIPIcs.FSTTCS.2025.32,
  author =	{Gangam, Rohith Reddy and Taherijam, Shayan and Vazirani, Vijay V.},
  title =	{{Fair Rent Division: New Budget and Rent Constraints}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.32},
  URN =		{urn:nbn:de:0030-drops-251136},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.32},
  annote =	{Keywords: Rent Division, Envy‑Free, Fair Division}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.15
Extending EFX Allocations to Further Multi-Graph Classes

Authors: Umang Bhaskar and Yeshwant Pandit

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The existence of EFX allocations is one of the most significant open questions in fair division. Recent work by Christodoulou, Fiat, Koutsoupias, and Sgouritsa ("Fair allocation in graphs," EC 2023) establishes the existence of EFX allocations for graphical valuations, when agents are vertices in a graph, items are edges, and each item has zero value for all agents other than those at its endpoints. Thus, in this setting, each good has non-zero value for at most two agents, and there is at most one good valued by any pair of agents. This marks one of the few cases when an exact and complete EFX allocation is known to exist for more than three agents. In this work, we partially extend these results to multi-graphs, when each pair of vertices can have more than one edge between them. The existence of EFX allocations in multi-graphs is a natural open question given their existence in simple graphs. We show that EFX allocations exist, and can be computed in polynomial time, for agents with cancelable valuations in the following cases: (i) bipartite multi-graphs, (ii) multi-trees with monotone valuations, and (iii) multi-graphs with girth (2t-1), where t is the chromatic number of the multi-graph. The existence of EFX in cycle multi-graphs follows from (i), (iii), and the known existence of EFX for three agents.
Cite as

Umang Bhaskar and Yeshwant Pandit. Extending EFX Allocations to Further Multi-Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhaskar_et_al:LIPIcs.FSTTCS.2025.15,
  author =	{Bhaskar, Umang and Pandit, Yeshwant},
  title =	{{Extending EFX Allocations to Further Multi-Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-250958},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.15},
  annote =	{Keywords: Fair Division, EFX, Multi-graphs}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.6
Explaining Reasoning Results for Description Logic Ontologies (Invited Paper)

Authors: Patrick Koopmann

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
The Web Ontology Language (OWL), grounded in description logics, enables reasoning systems to infer implicit knowledge in a transparent manner. However, the expressivity of description logics and the complexity of large ontologies often results in reasoning outcomes that are hard to understand without additional tool support. Explanations of these outcomes are essential for users to understand ontology content, communicate its structure and behavior effectively, and debug undesired or missing inferences. This chapter provides an overview of the central explanation techniques that have been developed for explaining reasoning with description logic ontologies. Here, we consider both explanations for positive entailments (explaining why something can be deduced), as well as negative entailments (why something cannot be deduced). More specifically, we discuss justifications, proofs and interpolation as a means to explain positive entailments, and abduction for explaining negative entailments, where we also have a closer look at practical algorithms as well as practical and theoretical challenges.
Cite as

Patrick Koopmann. Explaining Reasoning Results for Description Logic Ontologies (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 6:1-6:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koopmann:OASIcs.RW.2024/2025.6,
  author =	{Koopmann, Patrick},
  title =	{{Explaining Reasoning Results for Description Logic Ontologies}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{6:1--6:29},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.6},
  URN =		{urn:nbn:de:0030-drops-250514},
  doi =		{10.4230/OASIcs.RW.2024/2025.6},
  annote =	{Keywords: Explanations, Justifications, Proofs, Craig Interpolation, Contrastive Explanations}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.54
Reforming an Unfair Allocation by Exchanging Goods

Authors: Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong

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

Abstract
Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1.
Cite as

Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong. Reforming an Unfair Allocation by Exchanging Goods. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{yuen_et_al:LIPIcs.ISAAC.2025.54,
  author =	{Yuen, Sheung Man and Igarashi, Ayumi and Kamiyama, Naoyuki and Suksompong, Warut},
  title =	{{Reforming an Unfair Allocation by Exchanging Goods}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{54:1--54:21},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-249626},
  doi =		{10.4230/LIPIcs.ISAAC.2025.54},
  annote =	{Keywords: fair division, indivisible goods, envy-freeness, exchanges}
}
Document
DOI: 10.4230/OASIcs.DX.2025.1
Beyond Static Diagnosis: A Temporal ASP Framework for HVAC Fault Detection

Authors: Roxane Koitz-Hristov, Liliana Marie Prikler, and Franz Wotawa

Published in: OASIcs, Volume 136, 36th International Conference on Principles of Diagnosis and Resilient Systems (DX 2025)

Abstract
Improving sustainability in the building sector requires more efficient operation of energy-intensive systems such as Heating, Ventilation, and Air Conditioning (HVAC). We present a novel diagnostic framework for HVAC systems that integrates Answer Set Programming (ASP) with Functional Event Calculus (FEC). Our approach exploits the declarative nature of ASP for modeling and incorporates FEC to capture temporal system dynamics. We demonstrate the feasibility of our approach through a case study on a real-world heating system, where we model key components and system constraints. Our evaluation on nominal and faulty traces shows that exploiting ASP in combination with FEC can identify plausible diagnoses. Moreover, we explore the difference between static and rolling-window strategies and provide insights into runtime versus soundness on those variants. Our work provides a step toward the practical application of ASP-based temporal reasoning in building diagnostics.
Cite as

Roxane Koitz-Hristov, Liliana Marie Prikler, and Franz Wotawa. Beyond Static Diagnosis: A Temporal ASP Framework for HVAC Fault Detection. In 36th International Conference on Principles of Diagnosis and Resilient Systems (DX 2025). Open Access Series in Informatics (OASIcs), Volume 136, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koitzhristov_et_al:OASIcs.DX.2025.1,
  author =	{Koitz-Hristov, Roxane and Prikler, Liliana Marie and Wotawa, Franz},
  title =	{{Beyond Static Diagnosis: A Temporal ASP Framework for HVAC Fault Detection}},
  booktitle =	{36th International Conference on Principles of Diagnosis and Resilient Systems (DX 2025)},
  pages =	{1:1--1:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-394-2},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{136},
  editor =	{Quinones-Grueiro, Marcos and Biswas, Gautam and Pill, Ingo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.DX.2025.1},
  URN =		{urn:nbn:de:0030-drops-247901},
  doi =		{10.4230/OASIcs.DX.2025.1},
  annote =	{Keywords: Model-based diagnosis, Answer set programming, HVAC, Modeling for diagnosis, Experimental evaluation}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.36
Verifying Datalog Reasoning with Lean

Authors: Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Datalog is an essential logical rule language with many applications, and modern rule engines compute logical consequences for Datalog with high performance and scalability. While Datalog is rather simple and, in principle, explainable by design, such sophisticated implementations and optimizations are hard to verify. We therefore propose a certificate-based approach to validate results of Datalog reasoners in a formally verified checker for Datalog proofs. Using the proof assistant Lean, we implement such a checker and verify its correctness against direct formalizations of the Datalog semantics. We propose two JSON encodings for Datalog proofs: one using the widely supported Datalog proof trees, and one using directed acyclic graphs for succinctness. To evaluate the practical feasibility and performance of our approach, we validate proofs that we obtain by converting derivation traces of an existing Datalog reasoner into our tool-independent format.
Cite as

Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch. Verifying Datalog Reasoning with Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tantow_et_al:LIPIcs.ITP.2025.36,
  author =	{Tantow, Johannes and Gerlach, Lukas and Mennicke, Stephan and Kr\"{o}tzsch, Markus},
  title =	{{Verifying Datalog Reasoning with Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.36},
  URN =		{urn:nbn:de:0030-drops-246342},
  doi =		{10.4230/LIPIcs.ITP.2025.36},
  annote =	{Keywords: Certifying Algorithms, Datalog, Formal Verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.26
Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL

Authors: Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Sledgehammer is a tool that increases the level of automation in the Isabelle/HOL proof assistant by asking external automatic theorem provers (ATPs), including SMT solvers, to prove the current goal. When the external ATP succeeds it must provide enough evidence that the goal holds for Isabelle to be able to reprove it internally based on that evidence. In particular, Isabelle can do this by replaying fine-grained proof certificates from proof-producing SMT solvers as long as they are expressed in the Alethe format, which until now was supported only by the veriT SMT solver. We report on our experience adding proof reconstruction support for the cvc5 SMT solver in Isabelle by extending cvc5 to produce proofs in the Alethe format and then adapting Isabelle to reconstruct those proofs. We discuss several difficulties and pitfalls we encountered and describe a set of tools and techniques we developed to improve the process. A notable outcome of this effort is that Isabelle can now be used as an independent proof checker for SMT problems written in the SMT-LIB standard. We evaluate cvc5’s integration on a set of SMT-LIB benchmarks originating from Isabelle as well as on a set of Isabelle proofs. Our results confirm that this integration complements and improves Sledgehammer’s capabilities.
Cite as

Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli. Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lachnitt_et_al:LIPIcs.ITP.2025.26,
  author =	{Lachnitt, Hanna and Fleury, Mathias and Barbosa, Haniel and Jakpor, Jibiana and Andreotti, Bruno and Reynolds, Andrew and Schurr, Hans-J\"{o}rg and Barrett, Clark and Tinelli, Cesare},
  title =	{{Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.26},
  URN =		{urn:nbn:de:0030-drops-246243},
  doi =		{10.4230/LIPIcs.ITP.2025.26},
  annote =	{Keywords: interactive theorem proving, proof assistants, Isabelle/HOL, SMT, certification, proof certificates, proof reconstruction, proof automation}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
Cite as

Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.38
Reducing Quantum Circuit Synthesis to #SAT

Authors: Dekel Zak, Jingyi Mei, Jean-Marie Lagniez, and Alfons Laarman

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model counting, or #SAT, has recently been demonstrated as a promising new approach for tackling core problems in quantum circuit analysis. In this work, we show for the first time that the universal quantum circuit synthesis problem can be reduced to maximum model counting. We formulate a #SAT encoding for exact and approximate depth-optimal quantum circuit synthesis into the Clifford+T gate set. We evaluate our method with an open-source implementation that uses the maximum model counter d4Max as a backend. For this purpose, we extended d4Max with support for complex and negative weights to represent amplitudes. Experimental results show that existing classical tools have potential for the quantum circuit synthesis problem.
Cite as

Dekel Zak, Jingyi Mei, Jean-Marie Lagniez, and Alfons Laarman. Reducing Quantum Circuit Synthesis to #SAT. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zak_et_al:LIPIcs.CP.2025.38,
  author =	{Zak, Dekel and Mei, Jingyi and Lagniez, Jean-Marie and Laarman, Alfons},
  title =	{{Reducing Quantum Circuit Synthesis to #SAT}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.38},
  URN =		{urn:nbn:de:0030-drops-238997},
  doi =		{10.4230/LIPIcs.CP.2025.38},
  annote =	{Keywords: Maximum weighted model counting, quantum circuit synthesis}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.39
The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators

Authors: Tianwei Zhang and Stefan Szeider

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
We investigate the 3-decomposition conjecture, which states that every connected cubic graph can be decomposed into a spanning tree, a collection of cycles, and a matching. Using a SAT-based approach enhanced with specialized propagators, we verify the conjecture for all relevant graphs up to 28 vertices. Our method extends the Satisfiability Modulo Symmetries (SMS) framework with specialized propagators that exploit theoretical properties of minimal counterexamples (counterexamples with the minimal number of vertices), enabling efficient pruning. We demonstrate that graphs containing certain substructures cannot be minimal counterexamples to the conjecture, allowing us to exclude these patterns during the search dynamically. Our experimental results quantify the impact of different propagator configurations and forbidden subgraph constraints on solving efficiency, showing significant performance improvements when leveraging these techniques. The approach scales effectively to graphs of 28 vertices. Our work illustrates how combining SAT solving with specialized constraint propagation techniques can successfully address challenging combinatorial problems in contemporary graph theory.
Cite as

Tianwei Zhang and Stefan Szeider. The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.CP.2025.39,
  author =	{Zhang, Tianwei and Szeider, Stefan},
  title =	{{The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.39},
  URN =		{urn:nbn:de:0030-drops-239005},
  doi =		{10.4230/LIPIcs.CP.2025.39},
  annote =	{Keywords: SAT, Symmetry Breaking, Subgraphs, Propagators, Combinatorics}
}
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