12 Search Results for "Miller, Harvey"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.99
AC⁰[p]-Frege Cannot Efficiently Prove That Constant-Depth Algebraic Circuit Lower Bounds Are Hard

Authors: Jiaqi Lu, Rahul Santhanam, and Iddo Tzameret

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

Abstract
We study whether lower bounds against constant-depth algebraic circuits computing the Permanent over finite fields (Limaye-Srinivasan-Tavenas [J. ACM, 2025] and Forbes [CCC'24]) are hard to prove in certain proof systems. We focus on a DNF formula that expresses that such lower bounds are hard for constant-depth algebraic proofs. Using an adaptation of the diagonalization framework of Santhanam and Tzameret (SIAM J. Comput., 2025), we show unconditionally that this family of DNF formulas does not admit polynomial-size propositional AC⁰[p]-Frege proofs, infinitely often. This rules out the possibility that the DNF family is easy, and establishes that its status is either that of a hard tautology for AC⁰[p]-Frege or else unprovable (i.e., not a tautology). While it remains open whether the DNFs in question are tautologies, we provide evidence in this direction. In particular, under the plausible assumption that certain (weak) properties of multilinear algebra - specifically, those involving tensor rank - do not admit short constant-depth algebraic proofs, the DNFs are tautologies. We also observe that several weaker variants of the DNF formula are provably tautologies, and we show that the question of whether the DNFs are tautologies connects to conjectures of Razborov (ICALP'96) and Krajíček (J. Symb. Log., 2004). Additionally, our result has the following special features: ii) Existential depth amplification: the DNF formula considered is parameterised by a constant depth d bounding the depth of the algebraic proofs. We show that there exists some fixed depth d such that if there are no small depth-d algebraic proofs of certain circuit lower bounds for the Permanent, then there are no such small algebraic proofs in any constant depth. iii) Necessity: We show that our result is a necessary step towards establishing lower bounds against constant-depth algebraic proofs, and more generally against any sufficiently strong proof system. In particular, showing there are no short proofs for our DNF formulas, obtained by replacing "constant-depth algebraic circuits" with any "reasonable" algebraic circuit class C, is necessary in order to prove any super-polynomial lower bounds against algebraic proofs operating with circuits from C.
Cite as

Jiaqi Lu, Rahul Santhanam, and Iddo Tzameret. AC⁰[p]-Frege Cannot Efficiently Prove That Constant-Depth Algebraic Circuit Lower Bounds Are Hard. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 99:1-99:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lu_et_al:LIPIcs.ITCS.2026.99,
  author =	{Lu, Jiaqi and Santhanam, Rahul and Tzameret, Iddo},
  title =	{{AC⁰\lbrackp\rbrack-Frege Cannot Efficiently Prove That Constant-Depth Algebraic Circuit Lower Bounds Are Hard}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{99:1--99:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.99},
  URN =		{urn:nbn:de:0030-drops-253865},
  doi =		{10.4230/LIPIcs.ITCS.2026.99},
  annote =	{Keywords: Complexity, Lower bounds, Proof complexity, AC⁰\lbrackp\rbrack-Frege, Diagonalisation, Algebraic complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.3
Circle-Segment Intersection Queries in Connected Geometric Graphs

Authors: Peyman Afshani, Yannick Bosch, and Sabine Storandt

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

Abstract
In this paper, we study the problem of efficiently reporting all intersections between a given set of line segments in the plane and a query circle, focusing on the case where the segments form the edges of a connected geometric graph. While previous data structures for circle-segment intersection queries on general segment sets incur high space or query time costs, we exploit the connectivity of the input to obtain significantly improved performance. In fact, we propose a new circle-segment intersection data structure that can be constructed in 𝒪((n + C) log³ n) time and space on connected graphs with n edges and C edge crossings. It answers intersection queries in 𝒪(k log³ n) time, where k denotes the output size. Our method relies on the construction of efficient circle-graph intersection oracles as well as a novel linear-time algorithm to partition the edges of the graph into balanced, connected components, which might be of independent interest. In a proof-of-concept experimental study on real-world road networks, we show that our novel data structure also performs well in practice. Even on networks with millions of edges, the construction time is within minutes and queries are answered in a few milliseconds.
Cite as

Peyman Afshani, Yannick Bosch, and Sabine Storandt. Circle-Segment Intersection Queries in Connected Geometric Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{afshani_et_al:LIPIcs.ISAAC.2025.3,
  author =	{Afshani, Peyman and Bosch, Yannick and Storandt, Sabine},
  title =	{{Circle-Segment Intersection Queries in Connected Geometric Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{3:1--3:16},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-249114},
  doi =		{10.4230/LIPIcs.ISAAC.2025.3},
  annote =	{Keywords: Intersection data structure, Graph partitioning, Dobkin-Kirkpatrick hierarchy}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.TIME.2025.17
Visit Probability in Space-Time Prisms for Moving Object Data (Short Paper)

Authors: Arthur Jansen and Bart Kuijpers

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Space-time prisms have been extensively studied as a model to describe the uncertainty of the spatio-temporal location of a moving object in between measured space-time locations. In many applications, the desire has been expressed to provide an internal structure to these prisms, that includes what has been called "visit probability". Although several proposals have been studied in the past decades, a precise definition of this concept has been missing. The contribution of this paper is to provide such a specification by means of a formal framework for visit probability. Once this concept is established, we are able to derive on which parts of a prism, visit probability can be seen to give rise to a probability space.
Cite as

Arthur Jansen and Bart Kuijpers. Visit Probability in Space-Time Prisms for Moving Object Data (Short Paper). In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 17:1-17:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.TIME.2025.17,
  author =	{Jansen, Arthur and Kuijpers, Bart},
  title =	{{Visit Probability in Space-Time Prisms for Moving Object Data}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{17:1--17:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.17},
  URN =		{urn:nbn:de:0030-drops-244633},
  doi =		{10.4230/LIPIcs.TIME.2025.17},
  annote =	{Keywords: Spatio-temporal databases, moving object databases, space-time prisms, probability spaces}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.55
Safe Sequences via Dominators in DAGs for Path-Covering Problems

Authors: Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu

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

Abstract
A path-covering problem on a directed acyclic graph (DAG) requires finding a set of source-to-sink paths that cover all the nodes, all the arcs, or subsets thereof, and additionally they are optimal with respect to some function. In this paper we study safe sequences of nodes or arcs, namely sequences that appear in some path of every path cover of a DAG. We show that safe sequences admit a simple characterization via cutnodes. Moreover, we establish a connection between maximal safe sequences and leaf-to-root paths in the source- and sink-dominator trees of the DAG, which may be of independent interest in the extensive literature on dominators. With dominator trees, safe sequences admit an O(n)-size representation and a linear-time output-sensitive enumeration algorithm running in time O(m + o), where n and m are the number of nodes and arcs, respectively, and o is the total length of the maximal safe sequences. We then apply maximal safe sequences to simplify Integer Linear Programs (ILPs) for two path-covering problems, LeastSquares and MinPathError, which are at the core of RNA transcript assembly problems from bioinformatics. On various datasets, maximal safe sequences can be computed in under 0.1 seconds per graph, on average, and ILP solvers whose search space is reduced in this manner exhibit significant speed-ups. For example on graphs with a large width, average speed-ups are in the range 50-250× for MinPathError and in the range 80-350× for LeastSquares. Optimizing ILPs using safe sequences can thus become a fast building block of practical RNA transcript assembly tools, and more generally, of path-covering problems.
Cite as

Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu. Safe Sequences via Dominators in DAGs for Path-Covering Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sena_et_al:LIPIcs.ESA.2025.55,
  author =	{Sena, Francisco and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Safe Sequences via Dominators in DAGs for Path-Covering Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{55:1--55:17},
  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.2025.55},
  URN =		{urn:nbn:de:0030-drops-245230},
  doi =		{10.4230/LIPIcs.ESA.2025.55},
  annote =	{Keywords: directed acyclic graph, path cover, dominator tree, integer linear programming, least squares, minimum path error}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.29
The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration

Authors: Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron

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

Abstract
A dominating set of a graph G = (V,E) is a set of vertices D ⊆ V whose closed neighborhood is V, i.e., N[D] = V. We view a dominating set as a collection of tokens placed on the vertices of D. In the token sliding variant of the Dominating Set Reconfiguration problem (TS-DSR), we seek to transform a source dominating set into a target dominating set in G by sliding tokens along edges, and while maintaining a dominating set all along the transformation. TS-DSR is known to be PSPACE-complete even restricted to graphs of pathwidth w, for some non-explicit constant w and to be XL-complete parameterized by the size k of the solution. The first contribution of this article consists in using a novel approach to provide the first explicit constant for which the TS-DSR problem is PSPACE-complete, a question that was left open in the literature. From a parameterized complexity perspective, the token jumping variant of DSR, i.e., where tokens can jump to arbitrary vertices, is known to be FPT when parameterized by the size of the dominating sets on nowhere dense classes of graphs. But, in contrast, no non-trivial result was known about TS-DSR. We prove that DSR is actually much harder in the sliding model since it is XL-complete when restricted to bounded pathwidth graphs and even when parameterized by k plus the feedback vertex set number of the graph. This gives, for the first time, a difference of behavior between the complexity under token sliding and token jumping for some problem on graphs of bounded treewidth. All our results are obtained using a brand new method, based on the hardness of the so-called Tape Reconfiguration problem, a problem we believe to be of independent interest. We complement these hardness results with a positive result showing that DSR (parameterized by k) in the sliding model is FPT on planar graphs, also answering an open problem from the literature.
Cite as

Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron. The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.ESA.2025.29,
  author =	{Bousquet, Nicolas and Deschamps, Quentin and Mary, Arnaud and Mouawad, Amer E. and Pierron, Th\'{e}o},
  title =	{{The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{29:1--29:15},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-244974},
  doi =		{10.4230/LIPIcs.ESA.2025.29},
  annote =	{Keywords: combinatorial reconfiguration, parameterized complexity, structural graph parameters, treewidth, dominating set}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.36
Efficient Contractions of Dynamic Graphs - With Applications

Authors: Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke

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

Abstract
A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors. We discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs.
Cite as

Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke. Efficient Contractions of Dynamic Graphs - With Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.36,
  author =	{Henzinger, Monika and Kosinas, Evangelos and M\"{u}nk, Robin and R\"{a}cke, Harald},
  title =	{{Efficient Contractions of Dynamic Graphs - With Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{36:1--36:14},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-245047},
  doi =		{10.4230/LIPIcs.ESA.2025.36},
  annote =	{Keywords: Graph Algorithms, Cut Sparsifiers, Dynamic Algorithms}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2025.6
MODAP: A Multi-City Open Data & Analytics Platform for Micromobility Research

Authors: Grant McKenzie

Published in: LIPIcs, Volume 346, 13th International Conference on Geographic Information Science (GIScience 2025)

Abstract
Over the past decade, micromobility services, particularly electric vehicles for personal short-distance trips, have experienced significant growth. Major cities around the world now host extensive fleets of vehicles available for short-term public rental. While previous research has examined usage patterns within and between a few select cities, large, open, and publicly accessible data sets for analyzing mobility across multiple cities are extremely limited. I have collected, curated, and aggregated over twenty million e-scooter and e-bicycle trips across five major cities and are openly releasing aggregated data for use by mobility and sustainable transport researchers, urban planners, and policymakers. To accompany these data, I developed MODAP (Micromobility Open Data & Analytics Platform), a geovisual analytics tool that empowers researchers to explore the temporal and regional patterns of e-mobility trips within our open data set and download the data for offline analysis. My objective is to foster further research into city-scale mobility patterns and to equip researchers, community members, and policymakers with the necessary tools to conduct this work.
Cite as

Grant McKenzie. MODAP: A Multi-City Open Data & Analytics Platform for Micromobility Research. In 13th International Conference on Geographic Information Science (GIScience 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 346, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mckenzie:LIPIcs.GIScience.2025.6,
  author =	{McKenzie, Grant},
  title =	{{MODAP: A Multi-City Open Data \& Analytics Platform for Micromobility Research}},
  booktitle =	{13th International Conference on Geographic Information Science (GIScience 2025)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-378-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{346},
  editor =	{Sila-Nowicka, Katarzyna and Moore, Antoni and O'Sullivan, David and Adams, Benjamin and Gahegan, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2025.6},
  URN =		{urn:nbn:de:0030-drops-238353},
  doi =		{10.4230/LIPIcs.GIScience.2025.6},
  annote =	{Keywords: open data, mobility, geovisualization, micromobility}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.8
Breaking Symmetries with Involutions

Authors: Michael Codish and Mikoláš Janota

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

Abstract
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered too weak to be of practical use. Recently, the concept of graph patterns has been introduced and provides a concise representation for (large) sets of non-canonical graphs, i.e. graphs that are not lex-leaders and can be excluded from search. In particular, four (specific) graph patterns apply to identify about 3/4 of the set of all non-canonical graphs. Taking this approach further, we discover that graph patterns that derive from permutations that are involutions play an important role in the construction of symmetry breaks for graphs. We take advantage of this to guide the construction of partial and complete symmetry-breaking constraints based on graph patterns. The resulting constraints are small in size and strong in the number of symmetries they break.
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Michael Codish and Mikoláš Janota. Breaking Symmetries with Involutions. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{codish_et_al:LIPIcs.CP.2025.8,
  author =	{Codish, Michael and Janota, Mikol\'{a}\v{s}},
  title =	{{Breaking Symmetries with Involutions}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{8:1--8:17},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-238699},
  doi =		{10.4230/LIPIcs.CP.2025.8},
  annote =	{Keywords: graph symmetry, patterns, permutation, Ramsey graphs, greedy, CEGAR}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.18
q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations

Authors: Kiril Bangachev and S. Matthew Weinberg

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

Abstract
For a set M of m elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from 2^M to ℝ_{≥ 0}, parameterized by an integer q ∈ [2,m]. For a given q, we refer to the class as q-partitioning. A valuation function is subadditive if and only if it is 2-partitioning, and fractionally subadditive if and only if it is m-partitioning. Thus, our chain establishes an interpolation between subadditive and fractionally subadditive valuations. We show that this interpolation is smooth (q-partitioning valuations are "nearly" (q-1)-partitioning in a precise sense, Theorem 6), interpretable (the definition arises by analyzing the core of a cost-sharing game, à la the Bondareva-Shapley Theorem for fractionally subadditive valuations, Section 3.1), and non-trivial (the class of q-partitioning valuations is distinct for all q, Proposition 3). For domains where provable separations exist between subadditive and fractionally subadditive, we interpolate the stronger guarantees achievable for fractionally subadditive valuations to all q ∈ {2,…, m}. Two highlights are the following: 1) An Ω ((log log q)/(log log m))-competitive posted price mechanism for q-partitioning valuations. Note that this matches asymptotically the state-of-the-art for both subadditive (q = 2) [Paul Dütting et al., 2020], and fractionally subadditive (q = m) [Feldman et al., 2015]. 2) Two upper-tail concentration inequalities on 1-Lipschitz, q-partitioning valuations over independent items. One extends the state-of-the-art for q = m to q < m, the other improves the state-of-the-art for q = 2 for q > 2. Our concentration inequalities imply several corollaries that interpolate between subadditive and fractionally subadditive, for example: 𝔼[v(S)] ≤ (1 + 1/log q)Median[v(S)] + O(log q). To prove this, we develop a new isoperimetric inequality using Talagrand’s method of control by q points, which may be of independent interest. We also discuss other probabilistic inequalities and game-theoretic applications of q-partitioning valuations, and connections to subadditive MPH-k valuations [Tomer Ezra et al., 2019].
Cite as

Kiril Bangachev and S. Matthew Weinberg. q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bangachev_et_al:LIPIcs.ICALP.2025.18,
  author =	{Bangachev, Kiril and Weinberg, S. Matthew},
  title =	{{q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{18:1--18:20},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-233956},
  doi =		{10.4230/LIPIcs.ICALP.2025.18},
  annote =	{Keywords: Subadditive Functions, Fractionally Subadditive Functions, Posted Price Mechanisms, Concentration Inequalities}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.91
Incremental Approximate Maximum Flow via Residual Graph Sparsification

Authors: Gramoz Goranci, Monika Henzinger, Harald Räcke, and A. R. Sricharan

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

Abstract
We give an algorithm that, with high probability, maintains a (1-ε)-approximate s-t maximum flow in undirected, uncapacitated n-vertex graphs undergoing m edge insertions in Õ(m+ n F^*/ε) total update time, where F^{*} is the maximum flow on the final graph. This is the first algorithm to achieve polylogarithmic amortized update time for dense graphs (m = Ω(n²)), and more generally, for graphs where F^* = Õ(m/n). At the heart of our incremental algorithm is the residual graph sparsification technique of Karger and Levine [SICOMP '15], originally designed for computing exact maximum flows in the static setting. Our main contributions are (i) showing how to maintain such sparsifiers for approximate maximum flows in the incremental setting and (ii) generalizing the cut sparsification framework of Fung et al. [SICOMP '19] from undirected graphs to balanced directed graphs.
Cite as

Gramoz Goranci, Monika Henzinger, Harald Räcke, and A. R. Sricharan. Incremental Approximate Maximum Flow via Residual Graph Sparsification. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 91:1-91:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goranci_et_al:LIPIcs.ICALP.2025.91,
  author =	{Goranci, Gramoz and Henzinger, Monika and R\"{a}cke, Harald and Sricharan, A. R.},
  title =	{{Incremental Approximate Maximum Flow via Residual Graph Sparsification}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{91:1--91:20},
  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.2025.91},
  URN =		{urn:nbn:de:0030-drops-234686},
  doi =		{10.4230/LIPIcs.ICALP.2025.91},
  annote =	{Keywords: incremental flow, sparsification, approximate flow}
}
Document
DOI: 10.4230/DagSemProc.10491.7
10491 Results of the break-out group: Similarity measures

Authors: Joachim Gudmundsson, Harvey Miller, Rodrigo Silveira, Mathias Versichele, and Stefan van der Spek

Published in: Dagstuhl Seminar Proceedings, Volume 10491, Representation, Analysis and Visualization of Moving Objects (2011)

Abstract
In the group discussions we discussed distance measures focussing on real world applications specifically on domain areas where trajectories have been generated by animals (birds, primates...) and humans in urban areas.
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Joachim Gudmundsson, Harvey Miller, Rodrigo Silveira, Mathias Versichele, and Stefan van der Spek. 10491 Results of the break-out group: Similarity measures. In Representation, Analysis and Visualization of Moving Objects. Dagstuhl Seminar Proceedings, Volume 10491, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{gudmundsson_et_al:DagSemProc.10491.7,
  author =	{Gudmundsson, Joachim and Miller, Harvey and Silveira, Rodrigo and Versichele, Mathias and van der Spek, Stefan},
  title =	{{10491 Results of the break-out group: Similarity measures}},
  booktitle =	{Representation, Analysis and Visualization of Moving Objects},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2011},
  volume =	{10491},
  editor =	{J\"{o}rg-R\"{u}diger Sack and Bettina Speckmann and Emiel Van Loon and Robert Weibel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10491.7},
  URN =		{urn:nbn:de:0030-drops-29893},
  doi =		{10.4230/DagSemProc.10491.7},
  annote =	{Keywords: Similarity, Movement Analysis}
}
Document
DOI: 10.4230/DagSemProc.08471.2
Propagating and measuring anchor uncertainty in space-time prisms on road networks

Authors: Bart Kuijpers, Harvey J. Miller, Tijs Neutens, and Walied Othman

Published in: Dagstuhl Seminar Proceedings, Volume 8471, Geographic Privacy-Aware Knowledge Discovery and Delivery (2009)

Abstract
Space-time prisms capture all possible spatio-temporal locations of a moving object between sample points given speed limit constraints on its movement. These sample points are usually considered to be perfect measurements. In this paper we restrict ourselves to a road network and extend the notion of sample points to sample regions, which are bounded, sometimes disconnected, subsets of space-time wherein each point is a possible location, with its respective probability, where a moving object could have originated from or arrived in. This model allows us to model measurement errors, multiple possible simultaneous locations and even flexibility of a moving object. We develop an algorithm that computes the envelope of all space-time prisms that have an anchor in these sample regions and we developed an algorithm that computes for any spatio-temporal point the probability with which a space-time prism, with anchors in these sample regions, contains that point. We implemented these algorithms in Mathematica to visualise all these newly-introduced concepts.
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Bart Kuijpers, Harvey J. Miller, Tijs Neutens, and Walied Othman. Propagating and measuring anchor uncertainty in space-time prisms on road networks. In Geographic Privacy-Aware Knowledge Discovery and Delivery. Dagstuhl Seminar Proceedings, Volume 8471, pp. 1-35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kuijpers_et_al:DagSemProc.08471.2,
  author =	{Kuijpers, Bart and Miller, Harvey J. and Neutens, Tijs and Othman, Walied},
  title =	{{Propagating and measuring anchor uncertainty in space-time prisms on road networks}},
  booktitle =	{Geographic Privacy-Aware Knowledge Discovery and Delivery},
  pages =	{1--35},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8471},
  editor =	{Bart Kuijpers and Dino Pedreschi and Yucel Saygin and Stefano Spaccapietra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08471.2},
  URN =		{urn:nbn:de:0030-drops-20072},
  doi =		{10.4230/DagSemProc.08471.2},
  annote =	{Keywords: Space-time prisms, beads, prisms, uncertainty, flexibility, time-geography}
}
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