14 Search Results for "Kahn, David M."

Document
DOI: 10.4230/LIPIcs.ESA.2025.96
Counting Small Induced Subgraphs: Scorpions Are Easy but Not Trivial

Authors: Radu Curticapean, Simon Döring, and Daniel Neuen

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

Abstract
In the parameterized problem #IndSub(Φ) for fixed graph properties Φ, given as input a graph G and an integer k, the task is to compute the number of induced k-vertex subgraphs satisfying Φ. Dörfler et al. [Algorithmica 2022] and Roth et al. [SICOMP 2024] conjectured that #IndSub(Φ) is #W[1]-hard for all non-meager properties Φ, i.e., properties that are nontrivial for infinitely many k. This conjecture has been confirmed for several restricted types of properties, including all hereditary properties [STOC 2022] and all edge-monotone properties [STOC 2024]. We refute this conjecture by showing that induced k-vertex graphs that are scorpions can be counted in time O(n⁴) for all k. Scorpions were introduced more than 50 years ago in the context of the evasiveness conjecture. A simple variant of this construction results in graph properties that achieve arbitrary intermediate complexity assuming ETH. Moreover, we formulate an updated conjecture on the complexity of #IndSub(Φ) that correctly captures the complexity status of scorpions and related constructions.
Cite as

Radu Curticapean, Simon Döring, and Daniel Neuen. Counting Small Induced Subgraphs: Scorpions Are Easy but Not Trivial. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 96:1-96:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{curticapean_et_al:LIPIcs.ESA.2025.96,
  author =	{Curticapean, Radu and D\"{o}ring, Simon and Neuen, Daniel},
  title =	{{Counting Small Induced Subgraphs: Scorpions Are Easy but Not Trivial}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{96:1--96:16},
  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.2025.96},
  URN =		{urn:nbn:de:0030-drops-245651},
  doi =		{10.4230/LIPIcs.ESA.2025.96},
  annote =	{Keywords: induced subgraphs, counting complexity, parameterized complexity, scorpions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.25
Instance-Optimal Imprecise Convex Hull

Authors: Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong

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

Abstract
Imprecise measurements of a point set P = (p₁, …, p_n) can be modelled by a family of regions F = (R₁, …, R_n), where each imprecise region R_i ∈ F contains a unique point p_i ∈ P. A retrieval models an accurate measurement by replacing an imprecise region R_i with its corresponding point p_i. We construct the convex hull of an imprecise point set in the plane, by determining the cyclic ordering of the convex hull vertices of P as efficiently as possible. Efficiency is interpreted in two ways: (i) minimising the number of retrievals, and (ii) the computation time to determine the set of regions that must be retrieved. Previous works focused on only one of these two aspects: either minimising retrievals or optimising algorithmic runtime. Our contribution is the first to simultaneously achieve both. Let r(F, P) denote the minimal number of retrievals required by any algorithm to determine the convex hull of P for a given instance (F, P). For a family F of n constant-complexity polygons, our main result is a reconstruction algorithm that performs Θ(r(F, P)) retrievals in O(r(F, P) log³ n) time. Compared to previous approaches that achieve optimal retrieval counts, we improve the runtime per retrieval from polynomial to polylogarithmic. We extend the generality of previous results to simple k-gons, to pairwise disjoint disks with radii in [1,k], and to unit disks where at most k disks overlap in a single point. Our runtime scales linearly with k.
Cite as

Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong. Instance-Optimal Imprecise Convex Hull. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ESA.2025.25,
  author =	{de Berg, Sarita and van der Hoog, Ivor and Rotenberg, Eva and Rutschmann, Daniel and Wong, Sampson},
  title =	{{Instance-Optimal Imprecise Convex Hull}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{25:1--25:15},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-244932},
  doi =		{10.4230/LIPIcs.ESA.2025.25},
  annote =	{Keywords: convex hull, imprecise geometry preprocessing model, partial information}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.104
Optimal Antimatroid Sorting

Authors: Benjamin Aram Berendsohn

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

Abstract
The classical comparison-based sorting problem asks us to find the underlying total ordering of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a set T of possible total orderings is given, usually in some compressed form. Recently, an algorithm called topological heapsort with optimal running time was found for case where T is the set of topological orderings of a given directed acyclic graph, or, equivalently, T is the set of linear extensions of a partial ordering [Haeupler et al. 2024]. We show that a simple generalization of topological heapsort is applicable to a much broader class of restricted sorting problems, where T corresponds to a given antimatroid. As a consequence, we obtain optimal algorithms for the following restricted sorting problems, where the allowed total orders are … - … restricted by a given set of monotone precedence formulas; - … the perfect elimination orders of a given chordal graph; or - … the possible vertex search orders of a given connected rooted graph.
Cite as

Benjamin Aram Berendsohn. Optimal Antimatroid Sorting. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 104:1-104:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berendsohn:LIPIcs.ESA.2025.104,
  author =	{Berendsohn, Benjamin Aram},
  title =	{{Optimal Antimatroid Sorting}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{104:1--104:14},
  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.2025.104},
  URN =		{urn:nbn:de:0030-drops-245735},
  doi =		{10.4230/LIPIcs.ESA.2025.104},
  annote =	{Keywords: sorting, working-set heap, greedy, antimatroid}
}
Document
DOI: 10.4230/OASIcs.SpaceCHI.2025.10
A Postcard from Mars: Exploring Interplanetary Communications in Virtual Reality

Authors: Adalberto L. Simeone

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
In this paper we present an Immersive Speculative Enactment focused on the theme of interplanetary communications. These are a novel approach extending conventional Speculative Enactments to Virtual Reality. We created a narrative-based scenario in which participants played the role of human colonists on either Mars or the Moon, to explore a possible future in which interplanetary communication becomes a necessity. To enact this scenario, we created a VR interactive experience to elicit feedback on the idea of communicating across planets. Through an exploratory qualitative analysis of this immersive enactment, we found that while the future envisioned was seen as too distant to prompt realistic behaviour from all participants, the enactment helped us and the participants to reflect on the experience. We discuss these findings, drawing potential implications for the improvement of the feeling of "really being there" even in implausible situations and further contribute reflections on the role of ISEs in space-related scenarios.
Cite as

Adalberto L. Simeone. A Postcard from Mars: Exploring Interplanetary Communications in Virtual Reality. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{simeone:OASIcs.SpaceCHI.2025.10,
  author =	{Simeone, Adalberto L.},
  title =	{{A Postcard from Mars: Exploring Interplanetary Communications in Virtual Reality}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{10:1--10:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.10},
  URN =		{urn:nbn:de:0030-drops-240002},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.10},
  annote =	{Keywords: Immersive Speculative Enactments, Interplanetary Communications, Virtual Reality}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.76
Deciding Termination of Simple Randomized Loops

Authors: Éléanore Meyer and Jürgen Giesl

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all programs that consist of a single loop, with a linear loop guard and a loop body composed of two linear commuting and diagonalizable updates. In each iteration of the loop, the update to be carried out is picked at random, according to a fixed probability. We show the decidability of UPAST for this class of programs, where the program’s variables and inputs may range over various sub-semirings of the real numbers. In this way, we extend a line of research initiated by Tiwari in 2004 into the realm of randomized programs.
Cite as

Éléanore Meyer and Jürgen Giesl. Deciding Termination of Simple Randomized Loops. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 76:1-76:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{meyer_et_al:LIPIcs.MFCS.2025.76,
  author =	{Meyer, \'{E}l\'{e}anore and Giesl, J\"{u}rgen},
  title =	{{Deciding Termination of Simple Randomized Loops}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{76:1--76:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.76},
  URN =		{urn:nbn:de:0030-drops-241833},
  doi =		{10.4230/LIPIcs.MFCS.2025.76},
  annote =	{Keywords: decision procedures, randomized programs, linear loops, positive almost sure termination}
}
Document
DOI: 10.4230/LIPIcs.WABI.2025.10
DiVerG: Scalable Distance Index for Validation of Paired-End Alignments in Sequence Graphs

Authors: Ali Ghaffaari, Alexander Schönhuth, and Tobias Marschall

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract
Determining the distance between two loci within a genomic region is a recurrent operation in various tasks in computational genomics. A notable example of this task arises in paired-end read mapping as a form of validation of distances between multiple alignments. While straightforward for a single genome, graph-based reference structures render the operation considerably more involved. Given the sheer number of such queries in a typical read mapping experiment, an efficient algorithm for answering distance queries is crucial. In this paper, we introduce DiVerG, a compact data structure as well as a fast and scalable algorithm, for constructing distance indexes for general sequence graphs on multi-core CPU and many-core GPU architectures. DiVerG is based on PairG [Jain et al., 2019], but overcomes the limitations of PairG by exploiting the extensive potential for improvements in terms of scalability and space efficiency. As a consequence, DiVerG can process substantially larger datasets, such as whole human genomes, which are unmanageable by PairG. DiVerG offers faster index construction time and consistently faster query time with gains proportional to the size of the underlying compact data structure. We demonstrate that our method performs favorably on multiple real datasets at various scales. DiVerG achieves superior performance over PairG; e.g. resulting to 2.5-4x speed-up in query time, 44-340x smaller index size, and 3-50x faster construction time for the genome graph of the MHC region, as a particularly variable region of the human genome. The implementation is available at: https://github.com/cartoonist/diverg
Cite as

Ali Ghaffaari, Alexander Schönhuth, and Tobias Marschall. DiVerG: Scalable Distance Index for Validation of Paired-End Alignments in Sequence Graphs. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghaffaari_et_al:LIPIcs.WABI.2025.10,
  author =	{Ghaffaari, Ali and Sch\"{o}nhuth, Alexander and Marschall, Tobias},
  title =	{{DiVerG: Scalable Distance Index for Validation of Paired-End Alignments in Sequence Graphs}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{10:1--10:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.10},
  URN =		{urn:nbn:de:0030-drops-239369},
  doi =		{10.4230/LIPIcs.WABI.2025.10},
  annote =	{Keywords: Sequence graph, distance index, read mapping, sparse matrix}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.33
Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It

Authors: Sergei Stepanenko and Amin Timany

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Constructing solutions to recursive domain equations is a well-known, important problem in the study of programs and programming languages. Mathematically speaking, the problem is finding a fixed point (up to isomorphism) of a suitable functor over a suitable category. A particularly useful instance, inspired by the step-indexing technique, is where the functor is over (a subcategory of) the category of presheaves over the ordinal ω and the functors are locally-contractive, also known as guarded functors. This corresponds to step-indexing over natural numbers. However, for certain problems, e.g., when dealing with infinite non-determinism, one needs to employ trans-finite step-indexing, i.e., consider presheaf categories over higher ordinals. Prior work on trans-finite step-indexing either only considers a very narrow class of functors over a particularly restricted subcategory of presheaves over higher ordinals, or treats the problem very generally working with sheaves over an arbitrary complete Heyting algebra with a well-founded basis. In this paper we present a solution to the guarded domain equations problem over all guarded functors over the category of presheaves over ordinal numbers, as well as its mechanization in the Rocq Prover. As the categories of sheaves and presheaves over ordinals are equivalent, our main contribution is simplifying prior work from the setting of the category of sheaves to the setting of the category of presheaves and mechanizing it - presheaves are more amenable to mechanization in a proof assistant.
Cite as

Sergei Stepanenko and Amin Timany. Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{stepanenko_et_al:LIPIcs.FSCD.2025.33,
  author =	{Stepanenko, Sergei and Timany, Amin},
  title =	{{Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.33},
  URN =		{urn:nbn:de:0030-drops-236486},
  doi =		{10.4230/LIPIcs.FSCD.2025.33},
  annote =	{Keywords: Domain Equations, Guarded Fixed Points, Fixed Points, Category Theory, Rocq, Presheaves, Ordinals}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.47
Shelling and Sinking Graphs on the Sphere

Authors: Jeff Erickson and Christian Howard

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We describe a promising approach to efficiently morph spherical graphs, extending earlier approaches of Awartani and Henderson [Trans. AMS 1987] and Kobourov and Landis [JGAA 2006]. Specifically, we describe two methods to morph shortest-path triangulations of the sphere by moving their vertices along longitudes into the southern hemisphere; we call a triangulation sinkable if such a morph exists. Our first method generalizes a longitudinal shelling construction of Awartani and Henderson; a triangulation is sinkable if a specific orientation of its dual graph is acyclic. We describe a simple polynomial-time algorithm to find a longitudinally shellable rotation of a given spherical triangulation, if one exists; we also construct a spherical triangulation that has no longitudinally shellable rotation. Our second method is based on a linear-programming characterization of sinkability. By identifying its optimal basis, we show that this linear program can be solved in O(n^{ω/2}) time, where ω is the matrix-multiplication exponent, assuming the underlying linear system is non-singular. Finally, we pose several conjectures and describe experimental results that support them.
Cite as

Jeff Erickson and Christian Howard. Shelling and Sinking Graphs on the Sphere. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 47:1-47:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erickson_et_al:LIPIcs.SoCG.2025.47,
  author =	{Erickson, Jeff and Howard, Christian},
  title =	{{Shelling and Sinking Graphs on the Sphere}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{47:1--47:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.47},
  URN =		{urn:nbn:de:0030-drops-231996},
  doi =		{10.4230/LIPIcs.SoCG.2025.47},
  annote =	{Keywords: morphing, planar graphs, spherical graph drawing, longitudinal shelling}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.4
Hardness and Approximation Algorithms for Balanced Districting Problems

Authors: Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu

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

Abstract
We introduce and study the problem of balanced districting, where given an undirected graph with vertices carrying two types of weights (different population, resource types, etc) the goal is to maximize the total weights covered in vertex disjoint districts such that each district is a star or (in general) a connected induced subgraph with the two weights to be balanced. This problem is strongly motivated by political redistricting, where contiguity, population balance, and compactness are essential. We provide hardness and approximation algorithms for this problem. In particular, we show NP-hardness for an approximation better than n^{1/2-δ} for any constant δ > 0 in general graphs even when the districts are star graphs, as well as NP-hardness on complete graphs, tree graphs, planar graphs and other restricted settings. On the other hand, we develop an algorithm for balanced star districting that gives an O(√n)-approximation on any graph (which is basically tight considering matching hardness of approximation results), an O(log n) approximation on planar graphs with extensions to minor-free graphs. Our algorithm uses a modified Whack-a-Mole algorithm [Bhattacharya, Kiss, and Saranurak, SODA 2023] to find a sparse solution of a fractional packing linear program (despite exponentially many variables) which requires a new design of a separation oracle specific for our balanced districting problem. To turn the fractional solution to a feasible integer solution, we adopt the randomized rounding algorithm by [Chan and Har-Peled, SoCG 2009]. To get a good approximation ratio of the rounding procedure, a crucial element in the analysis is the balanced scattering separators for planar graphs and minor-free graphs - separators that can be partitioned into a small number of k-hop independent sets for some constant k - which may find independent interest in solving other packing style problems. Further, our algorithm is versatile - the very same algorithm can be analyzed in different ways on various graph classes, which leads to class-dependent approximation ratios. We also provide a FPTAS algorithm for complete graphs and tree graphs, as well as greedy algorithms and approximation ratios when the district cardinality is bounded, the graph has bounded degree or the weights are binary. We refer the readers to the full version of the paper for complete set of results and proofs.
Cite as

Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu. Hardness and Approximation Algorithms for Balanced Districting Problems. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dharangutte_et_al:LIPIcs.FORC.2025.4,
  author =	{Dharangutte, Prathamesh and Gao, Jie and Huang, Shang-En and Yu, Fang-Yi},
  title =	{{Hardness and Approximation Algorithms for Balanced Districting Problems}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{4:1--4:24},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-231310},
  doi =		{10.4230/LIPIcs.FORC.2025.4},
  annote =	{Keywords: Approximation algorithms, algorithmic fairness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.7
Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs

Authors: David C. Kutner and Anouk Sommer

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
In train networks, carefully-chosen delays may be beneficial for certain passengers, who would otherwise miss some connection. Given a simple (directed or undirected) temporal graph and a set of passengers (each specifying a starting vertex, an ending vertex, and a desired arrival time), we ask whether it is possible to delay some of the edges of the temporal graph to realize all the passengers' demands. We call this problem DelayBetter (DB), and study it along with two variants: in δ-DelayBetter, each delay must be of at most δ; in (δ-)Path DB, passengers also fully specify the vertices they should visit on their journey. On the positive side, we give a polynomial-time algorithm for Path DB and δ-Path DB, and obtain as a corollary a polynomial-time algorithm for DB and δ-DB on trees. We also provide an fpt algorithm for both problems parameterized by the size of the graph’s Feedback Edge Set together with the number of passengers. On the negative side, we show NP-completeness of (1-)DB on bounded-degree temporal graphs even when the lifetime is 2, and of (10-)DB on bounded-degree planar temporal graphs of lifetime 19. Our results complement previous work studying reachability problems in temporal graphs with delaying operations. This is to our knowledge the first such problem in which the aim is to facilitate travel between specific points (as opposed to facilitating or impeding a broadcast from one or many sources).
Cite as

David C. Kutner and Anouk Sommer. Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kutner_et_al:LIPIcs.SAND.2025.7,
  author =	{Kutner, David C. and Sommer, Anouk},
  title =	{{Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.7},
  URN =		{urn:nbn:de:0030-drops-230604},
  doi =		{10.4230/LIPIcs.SAND.2025.7},
  annote =	{Keywords: Temporal Graphs, Computational Complexity, Delay Management, Train Networks}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.57
Deterministic Approximation for the Volume of the Truncated Fractional Matching Polytope

Authors: Heng Guo and Vishvajeet N

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

Abstract
We give a deterministic polynomial-time approximation scheme (FPTAS) for the volume of the truncated fractional matching polytope for graphs of maximum degree Δ, where the truncation is by restricting each variable to the interval [0,(1+δ)/Δ], and δ ≤ C/Δ for some constant C > 0. We also generalise our result to the fractional matching polytope for hypergraphs of maximum degree Δ and maximum hyperedge size k, truncated by [0,(1+δ)/Δ] as well, where δ ≤ CΔ^{-(2k-3)/(k-1)}k^{-1} for some constant C > 0. The latter result generalises both the first result for graphs (when k = 2), and a result by Bencs and Regts (2024) for the truncated independence polytope (when Δ = 2). Our approach is based on the cluster expansion technique.
Cite as

Heng Guo and Vishvajeet N. Deterministic Approximation for the Volume of the Truncated Fractional Matching Polytope. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 57:1-57:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guo_et_al:LIPIcs.ITCS.2025.57,
  author =	{Guo, Heng and N, Vishvajeet},
  title =	{{Deterministic Approximation for the Volume of the Truncated Fractional Matching Polytope}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{57:1--57:14},
  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.2025.57},
  URN =		{urn:nbn:de:0030-drops-226858},
  doi =		{10.4230/LIPIcs.ITCS.2025.57},
  annote =	{Keywords: deterministic volume computation, cluster expansion, explicit polytopes}
}
Document
DOI: 10.4230/OASIcs.Gabbrielli.8
The Standard Model for Programming Languages: The Birth of a Mathematical Theory of Computation

Authors: Simone Martini

Published in: OASIcs, Volume 86, Recent Developments in the Design and Implementation of Programming Languages (2020)

Abstract
Despite the insight of some of the pioneers (Turing, von Neumann, Curry, Böhm), programming the early computers was a matter of fiddling with small architecture-dependent details. Only in the sixties some form of "mathematical program development" will be in the agenda of some of the most influential players of that time. A "Mathematical Theory of Computation" is the name chosen by John McCarthy for his approach, which uses a class of recursively computable functions as an (extensional) model of a class of programs. It is the beginning of that grand endeavour to present programming as a mathematical activity, and reasoning on programs as a form of mathematical logic. An important part of this process is the standard model of programming languages - the informal assumption that the meaning of programs should be understood on an abstract machine with unbounded resources, and with true arithmetic. We present some crucial moments of this story, concluding with the emergence, in the seventies, of the need of more "intensional" semantics, like the sequential algorithms on concrete data structures. The paper is a small step of a larger project - reflecting and tracing the interaction between mathematical logic and programming (languages), identifying some of the driving forces of this process. to Maurizio Gabbrielli, on his 60th birthday
Cite as

Simone Martini. The Standard Model for Programming Languages: The Birth of a Mathematical Theory of Computation. In Recent Developments in the Design and Implementation of Programming Languages. Open Access Series in Informatics (OASIcs), Volume 86, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{martini:OASIcs.Gabbrielli.8,
  author =	{Martini, Simone},
  title =	{{The Standard Model for Programming Languages: The Birth of a Mathematical Theory of Computation}},
  booktitle =	{Recent Developments in the Design and Implementation of Programming Languages},
  pages =	{8:1--8:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-171-9},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{86},
  editor =	{de Boer, Frank S. and Mauro, Jacopo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Gabbrielli.8},
  URN =		{urn:nbn:de:0030-drops-132307},
  doi =		{10.4230/OASIcs.Gabbrielli.8},
  annote =	{Keywords: Semantics of programming languages, history of programming languages, mathematical theory of computation}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.68
Undecidable Problems for Probabilistic Network Programming

Authors: David M. Kahn

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
The software-defined networking language NetKAT is able to verify many useful properties of networks automatically via a PSPACE decision procedure for program equality. However, for its probabilistic extension ProbNetKAT, no such decision procedure is known. We show that several potentially useful properties of ProbNetKAT are in fact undecidable, including emptiness of support intersection and certain kinds of distribution bounds and program comparisons. We do so by embedding the Post Correspondence Problem in ProbNetKAT via direct product expressions, and by directly embedding probabilistic finite automata.
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David M. Kahn. Undecidable Problems for Probabilistic Network Programming. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 68:1-68:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kahn:LIPIcs.MFCS.2017.68,
  author =	{Kahn, David M.},
  title =	{{Undecidable Problems for Probabilistic Network Programming}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{68:1--68:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.68},
  URN =		{urn:nbn:de:0030-drops-80969},
  doi =		{10.4230/LIPIcs.MFCS.2017.68},
  annote =	{Keywords: Software-defined networking, NetKAT, ProbNetKAT, Undecidability, Probabilistic finite automata}
}
Document
DOI: 10.4230/LITES-v002-i002-a001
From Dataflow Specification to Multiprocessor Partitioned Time-triggered Real-time Implementation

Authors: Thomas Carle, Dumitru Potop-Butucaru, Yves Sorel, and David Lesens

Published in: LITES, Volume 2, Issue 2 (2015). Leibniz Transactions on Embedded Systems, Volume 2, Issue 2

Abstract
Our objective is to facilitate the development of complex time-triggered systems by automating the allocation and scheduling steps. We show that full automation is possible while taking into account the elements of complexity needed by a complex embedded control system. More precisely, we consider deterministic functional specifications provided (as often in an industrial setting) by means of synchronous data-flow models with multiple modes and multiple relative periods. We first extend this functional model with an original real-time characterization that takes advantage of our time-triggered framework to provide a simpler representation of complex end-to-end flow requirements. We also extend our specifications with additional non-functional properties specifying partitioning, allocation, and preemptability constraints. Then, we provide novel algorithms for the off-line scheduling of these extended specifications onto partitioned time-triggered architectures à la ARINC 653. The main originality of our work is that it takes into account at the same time multiple complexity elements: various types of non-functional properties (real-time, partitioning, allocation, preemptability) and functional specifications with conditional execution and multiple modes. Allocation of time slots/windows to partitions can be fully or partially provided, or synthesized by our tool. Our algorithms allow the automatic allocation and scheduling onto multi-processor (distributed) systems with a global time base, taking into account communication costs. We demonstrate our technique on a model of space flight software system with strong real-time determinism requirements.
Cite as

Thomas Carle, Dumitru Potop-Butucaru, Yves Sorel, and David Lesens. From Dataflow Specification to Multiprocessor Partitioned Time-triggered Real-time Implementation. In LITES, Volume 2, Issue 2 (2015). Leibniz Transactions on Embedded Systems, Volume 2, Issue 2, pp. 01:1-01:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Article{carle_et_al:LITES-v002-i002-a001,
  author =	{Carle, Thomas and Potop-Butucaru, Dumitru and Sorel, Yves and Lesens, David},
  title =	{{From Dataflow Specification to Multiprocessor Partitioned Time-triggered Real-time Implementation}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{01:1--01:30},
  ISSN =	{2199-2002},
  year =	{2015},
  volume =	{2},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v002-i002-a001},
  URN =		{urn:nbn:de:0030-drops-192540},
  doi =		{10.4230/LITES-v002-i002-a001},
  annote =	{Keywords: Time-triggered, Off-line real-time scheduling, Temporal partitioning}
}
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