10 Search Results for "Xu, Jeff"

Document
DOI: 10.4230/LIPIcs.SEA.2024.20
Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks

Authors: Kenneth Langedal, Demian Hespe, and Peter Sanders

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Identifying a maximum independent set is a fundamental NP-hard problem. This problem has several real-world applications and requires finding the largest possible set of vertices not adjacent to each other in an undirected graph. Over the past few years, branch-and-bound and branch-and-reduce algorithms have emerged as some of the most effective methods for solving the problem exactly. Specifically, the branch-and-reduce approach, which combines branch-and-bound principles with reduction rules, has proven particularly successful in tackling previously unmanageable real-world instances. This progress was largely made possible by the development of more effective reduction rules. Nevertheless, other key components that can impact the efficiency of these algorithms have not received the same level of interest. Among these is the branching strategy, which determines which vertex to branch on next. Until recently, the most widely used strategy was to choose the vertex of the highest degree. In this work, we present a graph neural network approach for selecting the next branching vertex. The intricate nature of current branch-and-bound solvers makes supervised and reinforcement learning difficult. Therefore, we use a population-based genetic algorithm to evolve the model’s parameters instead. Our proposed approach results in a speedup on 73% of the benchmark instances with a median speedup of 24%.
Cite as

Kenneth Langedal, Demian Hespe, and Peter Sanders. Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{langedal_et_al:LIPIcs.SEA.2024.20,
  author =	{Langedal, Kenneth and Hespe, Demian and Sanders, Peter},
  title =	{{Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.20},
  URN =		{urn:nbn:de:0030-drops-203853},
  doi =		{10.4230/LIPIcs.SEA.2024.20},
  annote =	{Keywords: Graphs, Independent Set, Vertex Cover, Graph Neural Networks, Branch-and-Reduce}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.13
DeepTrust^RT: Confidential Deep Neural Inference Meets Real-Time!

Authors: Mohammad Fakhruddin Babar and Monowar Hasan

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
Deep Neural Networks (DNNs) are becoming common in "learning-enabled" time-critical applications such as autonomous driving and robotics. One approach to protect DNN inference from adversarial actions and preserve model privacy/confidentiality is to execute them within trusted enclaves available in modern processors. However, running DNN inference inside limited-capacity enclaves while ensuring timing guarantees is challenging due to (a) large size of DNN workloads and (b) extra switching between "normal" and "trusted" execution modes. This paper introduces new time-aware scheduling schemes - DeepTrust^RT - to securely execute deep neural inferences for learning-enabled real-time systems. We first propose a variant of EDF (called DeepTrust^RT-LW) that slices each DNN layer and runs them sequentially in the enclave. However, due to extra context switch overheads of individual layer slices, we further introduce a novel layer fusion technique (named DeepTrust^RT-FUSION). Our proposed scheme provides hard real-time guarantees by fusing multiple layers of DNN workload from multiple tasks; thus allowing them to fit and run concurrently within the enclaves while maintaining real-time guarantees. We implemented and tested DeepTrust^RT ideas on the Raspberry Pi platform running OP-TEE+DarkNet-TZ DNN APIs and three DNN workloads (AlexNet-squeezed, Tiny Darknet, YOLOv3-tiny). Compared to the layer-wise partitioning approach (DeepTrust^RT-LW), DeepTrust^RT-FUSION can schedule up to 3x more tasksets and reduce context switches by up to 11.12x. We further demonstrate the efficacy of DeepTrust^RT using a flight controller (ArduPilot) case study and find that DeepTrust^RT-FUSION retains real-time guarantees where DeepTrust^RT-LW becomes unschedulable.
Cite as

Mohammad Fakhruddin Babar and Monowar Hasan. DeepTrust^RT: Confidential Deep Neural Inference Meets Real-Time!. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 13:1-13:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{babar_et_al:LIPIcs.ECRTS.2024.13,
  author =	{Babar, Mohammad Fakhruddin and Hasan, Monowar},
  title =	{{DeepTrust^RT: Confidential Deep Neural Inference Meets Real-Time!}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{13:1--13:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.13},
  URN =		{urn:nbn:de:0030-drops-203161},
  doi =		{10.4230/LIPIcs.ECRTS.2024.13},
  annote =	{Keywords: DNN, TrustZone, Real-Time Systems}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.65
Optimal Electrical Oblivious Routing on Expanders

Authors: Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper, we investigate the question of whether the electrical flow routing is a good oblivious routing scheme on an m-edge graph G = (V, E) that is a Φ-expander, i.e. where |∂ S| ≥ Φ ⋅ vol(S) for every S ⊆ V, vol(S) ≤ vol(V)/2. Beyond its simplicity and structural importance, this question is well-motivated by the current state-of-the-art of fast algorithms for 𝓁_∞ oblivious routings that reduce to the expander-case which is in turn solved by electrical flow routing. Our main result proves that the electrical routing is an O(Φ^{-1} log m)-competitive oblivious routing in the 𝓁₁- and 𝓁_∞-norms. We further observe that the oblivious routing is O(log² m)-competitive in the 𝓁₂-norm and, in fact, O(log m)-competitive if 𝓁₂-localization is O(log m) which is widely believed. Using these three upper bounds, we can smoothly interpolate to obtain upper bounds for every p ∈ [2, ∞] and q given by 1/p + 1/q = 1. Assuming 𝓁₂-localization in O(log m), we obtain that in 𝓁_p and 𝓁_q, the electrical oblivious routing is O(Φ^{-(1-2/p)}log m) competitive. Using the currently known result for 𝓁₂-localization, this ratio deteriorates by at most a sublogarithmic factor for every p, q ≠ 2. We complement our upper bounds with lower bounds that show that the electrical routing for any such p and q is Ω(Φ^{-(1-2/p)} log m)-competitive. This renders our results in 𝓁₁ and 𝓁_∞ unconditionally tight up to constants, and the result in any 𝓁_p- and 𝓁_q-norm to be tight in case of 𝓁₂-localization in O(log m).
Cite as

Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva. Optimal Electrical Oblivious Routing on Expanders. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 65:1-65:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{florescu_et_al:LIPIcs.ICALP.2024.65,
  author =	{Florescu, Cella and Kyng, Rasmus and Gutenberg, Maximilian Probst and Sachdeva, Sushant},
  title =	{{Optimal Electrical Oblivious Routing on Expanders}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{65:1--65:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.65},
  URN =		{urn:nbn:de:0030-drops-202083},
  doi =		{10.4230/LIPIcs.ICALP.2024.65},
  annote =	{Keywords: Expanders, Oblivious routing for 𝓁\underlinep, Electrical flow routing}
}
Document
DOI: 10.4230/DagMan.10.1.1
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.
Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.71
Beyond Chromatic Threshold via (p,q)-Theorem, and Blow-Up Phenomenon

Authors: Hong Liu, Chong Shangguan, Jozef Skokan, and Zixiang Xu

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
We establish a novel connection between the well-known chromatic threshold problem in extremal combinatorics and the celebrated (p,q)-theorem in discrete geometry. In particular, for a graph G with bounded clique number and a natural density condition, we prove a (p,q)-theorem for an abstract convexity space associated with G. Our result strengthens those of Thomassen and Nikiforov on the chromatic threshold of cliques. Our (p,q)-theorem can also be viewed as a χ-boundedness result for (what we call) ultra maximal K_r-free graphs. We further show that the graphs under study are blow-ups of constant size graphs, improving a result of Oberkampf and Schacht on homomorphism threshold of cliques. Our result unravels the cause underpinning such a blow-up phenomenon, differentiating the chromatic and homomorphism threshold problems for cliques. Our result implies that for the homomorphism threshold problem, rather than the minimum degree condition usually considered in the literature, the decisive factor is a clique density condition on co-neighborhoods of vertices. More precisely, we show that if an n-vertex K_r-free graph G satisfies that the common neighborhood of every pair of non-adjacent vertices induces a subgraph with K_{r-2}-density at least ε > 0, then G must be a blow-up of some K_r-free graph F on at most 2^O(r/ε log1/ε) vertices. Furthermore, this single exponential bound is optimal. We construct examples with no K_r-free homomorphic image of size smaller than 2^Ω_r(1/ε).
Cite as

Hong Liu, Chong Shangguan, Jozef Skokan, and Zixiang Xu. Beyond Chromatic Threshold via (p,q)-Theorem, and Blow-Up Phenomenon. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 71:1-71:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{liu_et_al:LIPIcs.SoCG.2024.71,
  author =	{Liu, Hong and Shangguan, Chong and Skokan, Jozef and Xu, Zixiang},
  title =	{{Beyond Chromatic Threshold via (p,q)-Theorem, and Blow-Up Phenomenon}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{71:1--71:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.71},
  URN =		{urn:nbn:de:0030-drops-200162},
  doi =		{10.4230/LIPIcs.SoCG.2024.71},
  annote =	{Keywords: (p,q)-theorem, fractional Helly number, weak \epsilon-net, chromatic threshold, VC dimension}
}
Document
Position
DOI: 10.4230/TGDK.2.1.2
Grounding Stream Reasoning Research

Authors: Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
In the last decade, there has been a growing interest in applying AI technologies to implement complex data analytics over data streams. To this end, researchers in various fields have been organising a yearly event called the "Stream Reasoning Workshop" to share perspectives, challenges, and experiences around this topic. In this paper, the previous organisers of the workshops and other community members provide a summary of the main research results that have been discussed during the first six editions of the event. These results can be categorised into four main research areas: The first is concerned with the technological challenges related to handling large data streams. The second area aims at adapting and extending existing semantic technologies to data streams. The third and fourth areas focus on how to implement reasoning techniques, either considering deductive or inductive techniques, to extract new and valuable knowledge from the data in the stream. This summary is written not only to provide a crystallisation of the field, but also to point out distinctive traits of the stream reasoning community. Moreover, it also provides a foundation for future research by enumerating a list of use cases and open challenges, to stimulate others to join this exciting research area.
Cite as

Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer. Grounding Stream Reasoning Research. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 2:1-2:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{bonte_et_al:TGDK.2.1.2,
  author =	{Bonte, Pieter and Calbimonte, Jean-Paul and de Leng, Daniel and Dell'Aglio, Daniele and Della Valle, Emanuele and Eiter, Thomas and Giannini, Federico and Heintz, Fredrik and Schekotihin, Konstantin and Le-Phuoc, Danh and Mileo, Alessandra and Schneider, Patrik and Tommasini, Riccardo and Urbani, Jacopo and Ziffer, Giacomo},
  title =	{{Grounding Stream Reasoning Research}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:47},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.2},
  URN =		{urn:nbn:de:0030-drops-198597},
  doi =		{10.4230/TGDK.2.1.2},
  annote =	{Keywords: Stream Reasoning, Stream Processing, RDF streams, Streaming Linked Data, Continuous query processing, Temporal Logics, High-performance computing, Databases}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.3
Semantic Web: Past, Present, and Future

Authors: Ansgar Scherp, Gerd Groener, Petr Škoda, Katja Hose, and Maria-Esther Vidal

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Ever since the vision was formulated, the Semantic Web has inspired many generations of innovations. Semantic technologies have been used to share vast amounts of information on the Web, enhance them with semantics to give them meaning, and enable inference and reasoning on them. Throughout the years, semantic technologies, and in particular knowledge graphs, have been used in search engines, data integration, enterprise settings, and machine learning. In this paper, we recap the classical concepts and foundations of the Semantic Web as well as modern and recent concepts and applications, building upon these foundations. The classical topics we cover include knowledge representation, creating and validating knowledge on the Web, reasoning and linking, and distributed querying. We enhance this classical view of the so-called "Semantic Web Layer Cake" with an update of recent concepts that include provenance, security and trust, as well as a discussion of practical impacts from industry-led contributions. We conclude with an outlook on the future directions of the Semantic Web. This is a living document. If you like to contribute, please contact the first author and visit: https://github.com/ascherp/semantic-web-primer
Cite as

Ansgar Scherp, Gerd Groener, Petr Škoda, Katja Hose, and Maria-Esther Vidal. Semantic Web: Past, Present, and Future. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 3:1-3:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{scherp_et_al:TGDK.2.1.3,
  author =	{Scherp, Ansgar and Groener, Gerd and \v{S}koda, Petr and Hose, Katja and Vidal, Maria-Esther},
  title =	{{Semantic Web: Past, Present, and Future}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:37},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.3},
  URN =		{urn:nbn:de:0030-drops-198607},
  doi =		{10.4230/TGDK.2.1.3},
  annote =	{Keywords: Linked Open Data, Semantic Web Graphs, Knowledge Graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.78
Ellipsoid Fitting up to a Constant

Authors: Jun-Ting Hsieh, Pravesh K. Kothari, Aaron Potechin, and Jeff Xu

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
In [Saunderson, 2011; Saunderson et al., 2013], Saunderson, Parrilo, and Willsky asked the following elegant geometric question: what is the largest m = m(d) such that there is an ellipsoid in ℝ^d that passes through v_1, v_2, …, v_m with high probability when the v_is are chosen independently from the standard Gaussian distribution N(0,I_d)? The existence of such an ellipsoid is equivalent to the existence of a positive semidefinite matrix X such that v_i^⊤ X v_i = 1 for every 1 ⩽ i ⩽ m - a natural example of a random semidefinite program. SPW conjectured that m = (1-o(1)) d²/4 with high probability. Very recently, Potechin, Turner, Venkat and Wein [Potechin et al., 2022] and Kane and Diakonikolas [Kane and Diakonikolas, 2022] proved that m ≳ d²/log^O(1) d via a certain natural, explicit construction. In this work, we give a substantially tighter analysis of their construction to prove that m ≳ d²/C for an absolute constant C > 0. This resolves one direction of the SPW conjecture up to a constant. Our analysis proceeds via the method of Graphical Matrix Decomposition that has recently been used to analyze correlated random matrices arising in various areas [Barak et al., 2019; Bafna et al., 2022]. Our key new technical tool is a refined method to prove singular value upper bounds on certain correlated random matrices that are tight up to absolute dimension-independent constants. In contrast, all previous methods that analyze such matrices lose logarithmic factors in the dimension.
Cite as

Jun-Ting Hsieh, Pravesh K. Kothari, Aaron Potechin, and Jeff Xu. Ellipsoid Fitting up to a Constant. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hsieh_et_al:LIPIcs.ICALP.2023.78,
  author =	{Hsieh, Jun-Ting and Kothari, Pravesh K. and Potechin, Aaron and Xu, Jeff},
  title =	{{Ellipsoid Fitting up to a Constant}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{78:1--78:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.78},
  URN =		{urn:nbn:de:0030-drops-181304},
  doi =		{10.4230/LIPIcs.ICALP.2023.78},
  annote =	{Keywords: Semidefinite programming, random matrices, average-case complexity}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.11
Certifying Solution Geometry in Random CSPs: Counts, Clusters and Balance

Authors: Jun-Ting Hsieh, Sidhanth Mohanty, and Jeff Xu

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been made via statistical physics-based heuristics. In parallel, there has been a recent flurry of work on refuting random constraint satisfaction problems, via nailing refutation thresholds for spectral and semidefinite programming-based algorithms, and also on counting solutions to CSPs. Inspired by this, the starting point for our work is the following question: What does the solution space for a random CSP look like to an efficient algorithm? In pursuit of this inquiry, we focus on the following problems about random Boolean CSPs at the densities where they are unsatisfiable but no refutation algorithm is known. 1) Counts. For every Boolean CSP we give algorithms that with high probability certify a subexponential upper bound on the number of solutions. We also give algorithms to certify a bound on the number of large cuts in a Gaussian-weighted graph, and the number of large independent sets in a random d-regular graph. 2) Clusters. For Boolean 3CSPs we give algorithms that with high probability certify an upper bound on the number of clusters of solutions. 3) Balance. We also give algorithms that with high probability certify that there are no "unbalanced" solutions, i.e., solutions where the fraction of +1s deviates significantly from 50%. Finally, we also provide hardness evidence suggesting that our algorithms for counting are optimal.
Cite as

Jun-Ting Hsieh, Sidhanth Mohanty, and Jeff Xu. Certifying Solution Geometry in Random CSPs: Counts, Clusters and Balance. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hsieh_et_al:LIPIcs.CCC.2022.11,
  author =	{Hsieh, Jun-Ting and Mohanty, Sidhanth and Xu, Jeff},
  title =	{{Certifying Solution Geometry in Random CSPs: Counts, Clusters and Balance}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.11},
  URN =		{urn:nbn:de:0030-drops-165735},
  doi =		{10.4230/LIPIcs.CCC.2022.11},
  annote =	{Keywords: constraint satisfaction problems, certified counting, random graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.8
Recognizing Weakly Simple Polygons

Authors: Hugo A. Akitaya, Greg Aloupis, Jeff Erickson, and Csaba Tóth

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
We present an O(n log n)-time algorithm that determines whether a given planar n-gon is weakly simple. This improves upon an O(n^2 log n)-time algorithm by [Chang, Erickson, and Xu, SODA, 2015]. Weakly simple polygons are required as input for several geometric algorithms. As such, how to recognize simple or weakly simple polygons is a fundamental question.
Cite as

Hugo A. Akitaya, Greg Aloupis, Jeff Erickson, and Csaba Tóth. Recognizing Weakly Simple Polygons. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{akitaya_et_al:LIPIcs.SoCG.2016.8,
  author =	{Akitaya, Hugo A. and Aloupis, Greg and Erickson, Jeff and T\'{o}th, Csaba},
  title =	{{Recognizing Weakly Simple Polygons}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.8},
  URN =		{urn:nbn:de:0030-drops-59003},
  doi =		{10.4230/LIPIcs.SoCG.2016.8},
  annote =	{Keywords: weakly simple polygon, crossing}
}
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