9 Search Results for "Wilson, James B."

Document
DOI: 10.4230/OASIcs.ATMOS.2024.17
Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities

Authors: Tobias Harks, Sven Jäger, Michael Markl, and Philine Schiewe

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

Abstract
Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model for passenger assignments is to integrate selfish routing behaviour of passengers on the one hand, and the limited vehicle capacities on the other hand. We formulate a side-constrained user equilibrium model in a schedule-based time-expanded transit network, where passengers are modelled via a continuum of non-atomic agents that want to travel with a fixed start time from a user-specific origin to a destination. An agent’s route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence by generalizing a well-known existence result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances and an exact finite time algorithm for the multi-commodity case. Based on our quasi-variational characterization, we finally devise a fast heuristic computing user equilibria, which is tested on real-world instances based on data gained from the Hamburg S-Bahn system and the Swiss long-distance train network. It turns out that w.r.t. the total travel time, the computed user-equilibria are quite efficient compared to a system optimum, which neglects equilibrium constraints and only minimizes total travel time.
Cite as

Tobias Harks, Sven Jäger, Michael Markl, and Philine Schiewe. Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harks_et_al:OASIcs.ATMOS.2024.17,
  author =	{Harks, Tobias and J\"{a}ger, Sven and Markl, Michael and Schiewe, Philine},
  title =	{{Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{17:1--17:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.17},
  URN =		{urn:nbn:de:0030-drops-212054},
  doi =		{10.4230/OASIcs.ATMOS.2024.17},
  annote =	{Keywords: traffic assignment, side-constrained equilibrium, public transportation}
}
Document
DOI: 10.4230/OASIcs.ICPEC.2024.6
An Experience with Adaptive Formative Assessment for Motivating Novices in Introductory Programming Learning

Authors: Jagadeeswaran Thangaraj, Monica Ward, and Fiona O’Riordan

Published in: OASIcs, Volume 122, 5th International Computer Programming Education Conference (ICPEC 2024)

Abstract
This study presents empirical research that uses adaptive formative assessment framework in addition to traditional lectures to motivate novice students in an introductory programming course. The primary goal of this work is to provide guidance for the creation of adaptive formative assessments in Python programming language to inspire novice students. The experiment is based on lessons learned from the literature and pedagogical theories that support learning through assessment and scaffolding. This study investigates how the experiment helped the novices, whether it increased their confidence, whether it assisted in identifying and correcting common errors, and whether it covered the material on learning modular programming components. It report on extensive survey results of over 265 attempts of 90 students taking CS1 (introductory programming) that included five quizzes covering fundamental concepts. The students responded favorably to the experiment, and results are also included.
Cite as

Jagadeeswaran Thangaraj, Monica Ward, and Fiona O’Riordan. An Experience with Adaptive Formative Assessment for Motivating Novices in Introductory Programming Learning. In 5th International Computer Programming Education Conference (ICPEC 2024). Open Access Series in Informatics (OASIcs), Volume 122, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{thangaraj_et_al:OASIcs.ICPEC.2024.6,
  author =	{Thangaraj, Jagadeeswaran and Ward, Monica and O’Riordan, Fiona},
  title =	{{An Experience with Adaptive Formative Assessment for Motivating Novices in Introductory Programming Learning}},
  booktitle =	{5th International Computer Programming Education Conference (ICPEC 2024)},
  pages =	{6:1--6:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-347-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{122},
  editor =	{Santos, Andr\'{e} L. and Pinto-Albuquerque, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICPEC.2024.6},
  URN =		{urn:nbn:de:0030-drops-209755},
  doi =		{10.4230/OASIcs.ICPEC.2024.6},
  annote =	{Keywords: Assessment and feedback, Computer programming, CS1, Formative assessment, Introductory programming, Novice students}
}
Document
DOI: 10.4230/OASIcs.ICPEC.2024.20
Use of Programming Aids in Undergraduate Courses

Authors: Ana Rita Peixoto, André Glória, José Luís Silva, Maria Pinto-Albuquerque, Tomás Brandão, and Luís Nunes

Published in: OASIcs, Volume 122, 5th International Computer Programming Education Conference (ICPEC 2024)

Abstract
The use of external tips and applications to help with programming assignments, by novice programmers, is a double-edged sword, it can help by showing examples of problem-solving strategies, but it can also prevent learning because recognizing a good solution is not the same skill as creating one. A study was conducted during the 2superscript{nd} semester of 23/24 in the course of Object Oriented Programming to help understand the impact of the programming aids in learning. The main questions that drove this study were: Which type(s) of assistance do students use when learning to program? When / where do they use it? Does it affect grades? Results, even though with a relatively small sample, seem to indicate that students who used aids have a perception of improved learning when using advice from Colleagues, Copilot-style tools, and Large Language Models. Results of correlating average grades with the usage of tools suggest that experience in using these tools is key for its successful use, but, contrary to students' perceptions, learning gains are marginal in the end result.
Cite as

Ana Rita Peixoto, André Glória, José Luís Silva, Maria Pinto-Albuquerque, Tomás Brandão, and Luís Nunes. Use of Programming Aids in Undergraduate Courses. In 5th International Computer Programming Education Conference (ICPEC 2024). Open Access Series in Informatics (OASIcs), Volume 122, pp. 20:1-20:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{peixoto_et_al:OASIcs.ICPEC.2024.20,
  author =	{Peixoto, Ana Rita and Gl\'{o}ria, Andr\'{e} and Silva, Jos\'{e} Lu{\'\i}s and Pinto-Albuquerque, Maria and Brand\~{a}o, Tom\'{a}s and Nunes, Lu{\'\i}s},
  title =	{{Use of Programming Aids in Undergraduate Courses}},
  booktitle =	{5th International Computer Programming Education Conference (ICPEC 2024)},
  pages =	{20:1--20:9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-347-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{122},
  editor =	{Santos, Andr\'{e} L. and Pinto-Albuquerque, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICPEC.2024.20},
  URN =		{urn:nbn:de:0030-drops-209894},
  doi =		{10.4230/OASIcs.ICPEC.2024.20},
  annote =	{Keywords: Teaching Programming, Programming aids}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.13
Improved Bounds of Integer Solution Counts via Volume and Extending to Mixed-Integer Linear Constraints

Authors: Cunjing Ge and Armin Biere

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Solution counting and solution space integration over linear constraints are important problems with many applications. Previous works addressed either only counting integer points in polytopes (integer counting) with integer variables or alternatively only computing the volume of polytopes (solution space integration) on variables over the reals, including approximating the integer count via a polytope’s volume. We are not aware of a non-trivial algorithm which addresses the mixed case, where linear constraints are over mixed integer and real variables. In this paper, we propose a new randomized algorithm to approximate guarantees (bounds) of integer solution counts. Then we present upper and lower bounds for solution space integration over mixed-integer linear constraints. Thus, proposed algorithms can be extended to mixed-integer cases as well. The experiments show that approximations are often very close to exact results in practice, and bounds approximated by our algorithm are often tight and useful.
Cite as

Cunjing Ge and Armin Biere. Improved Bounds of Integer Solution Counts via Volume and Extending to Mixed-Integer Linear Constraints. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ge_et_al:LIPIcs.CP.2024.13,
  author =	{Ge, Cunjing and Biere, Armin},
  title =	{{Improved Bounds of Integer Solution Counts via Volume and Extending to Mixed-Integer Linear Constraints}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.13},
  URN =		{urn:nbn:de:0030-drops-206983},
  doi =		{10.4230/LIPIcs.CP.2024.13},
  annote =	{Keywords: Integer Solution Counting, Mixed-Integer Linear Constraints, #SMT(LA) Problems, Volume of Polytopes}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.20
Constraint Modelling with LLMs Using In-Context Learning

Authors: Kostis Michailidis, Dimos Tsouros, and Tias Guns

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Constraint Programming (CP) allows for the modelling and solving of a wide range of combinatorial problems. However, modelling such problems using constraints over decision variables still requires significant expertise, both in conceptual thinking and syntactic use of modelling languages. In this work, we explore the potential of using pre-trained Large Language Models (LLMs) as coding assistants, to transform textual problem descriptions into concrete and executable CP specifications. We present different transformation pipelines with explicit intermediate representations, and we investigate the potential benefit of various retrieval-augmented example selection strategies for in-context learning. We evaluate our approach on 2 datasets from the literature, namely NL4Opt (optimisation) and Logic Grid Puzzles (satisfaction), and a heterogeneous set of exercises from a CP course. The results show that pre-trained LLMs have promising potential for initialising the modelling process, with retrieval-augmented in-context learning significantly enhancing their modelling capabilities.
Cite as

Kostis Michailidis, Dimos Tsouros, and Tias Guns. Constraint Modelling with LLMs Using In-Context Learning. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 20:1-20:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{michailidis_et_al:LIPIcs.CP.2024.20,
  author =	{Michailidis, Kostis and Tsouros, Dimos and Guns, Tias},
  title =	{{Constraint Modelling with LLMs Using In-Context Learning}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{20:1--20:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.20},
  URN =		{urn:nbn:de:0030-drops-207053},
  doi =		{10.4230/LIPIcs.CP.2024.20},
  annote =	{Keywords: Constraint Modelling, Constraint Acquisition, Constraint Programming, Large Language Models, In-Context Learning, Natural Language Processing, Named Entity Recognition, Retrieval-Augmented Generation, Optimisation}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.16
On p-Group Isomorphism: Search-To-Decision, Counting-To-Decision, and Nilpotency Class Reductions via Tensors

Authors: Joshua A. Grochow and Youming Qiao

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
In this paper we study some classical complexity-theoretic questions regarding Group Isomorphism (GpI). We focus on p-groups (groups of prime power order) with odd p, which are believed to be a bottleneck case for GpI, and work in the model of matrix groups over finite fields. Our main results are as follows. - Although search-to-decision and counting-to-decision reductions have been known for over four decades for Graph Isomorphism (GI), they had remained open for GpI, explicitly asked by Arvind & Torán (Bull. EATCS, 2005). Extending methods from Tensor Isomorphism (Grochow & Qiao, ITCS 2021), we show moderately exponential-time such reductions within p-groups of class 2 and exponent p. - Despite the widely held belief that p-groups of class 2 and exponent p are the hardest cases of GpI, there was no reduction to these groups from any larger class of groups. Again using methods from Tensor Isomorphism (ibid.), we show the first such reduction, namely from isomorphism testing of p-groups of "small" class and exponent p to those of class two and exponent p. For the first results, our main innovation is to develop linear-algebraic analogues of classical graph coloring gadgets, a key technique in studying the structural complexity of GI. Unlike the graph coloring gadgets, which support restricting to various subgroups of the symmetric group, the problems we study require restricting to various subgroups of the general linear group, which entails significantly different and more complicated gadgets. The analysis of one of our gadgets relies on a classical result from group theory regarding random generation of classical groups (Kantor & Lubotzky, Geom. Dedicata, 1990). For the nilpotency class reduction, we combine a runtime analysis of the Lazard Correspondence with Tensor Isomorphism-completeness results (Grochow & Qiao, ibid.).
Cite as

Joshua A. Grochow and Youming Qiao. On p-Group Isomorphism: Search-To-Decision, Counting-To-Decision, and Nilpotency Class Reductions via Tensors. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 16:1-16:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{grochow_et_al:LIPIcs.CCC.2021.16,
  author =	{Grochow, Joshua A. and Qiao, Youming},
  title =	{{On p-Group Isomorphism: Search-To-Decision, Counting-To-Decision, and Nilpotency Class Reductions via Tensors}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{16:1--16:38},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.16},
  URN =		{urn:nbn:de:0030-drops-142905},
  doi =		{10.4230/LIPIcs.CCC.2021.16},
  annote =	{Keywords: group isomorphism, search-to-decision reduction, counting-to-decision reduction, nilpotent group isomorphism, p-group isomorphism, tensor isomorphism}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.31
On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness

Authors: Joshua A. Grochow and Youming Qiao

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We study the complexity of isomorphism problems for tensors, groups, and polynomials. These problems have been studied in multivariate cryptography, machine learning, quantum information, and computational group theory. We show that these problems are all polynomial-time equivalent, creating bridges between problems traditionally studied in myriad research areas. This prompts us to define the complexity class TI, namely problems that reduce to the Tensor Isomorphism (TI) problem in polynomial time. Our main technical result is a polynomial-time reduction from d-tensor isomorphism to 3-tensor isomorphism. In the context of quantum information, this result gives multipartite-to-tripartite entanglement transformation procedure, that preserves equivalence under stochastic local operations and classical communication (SLOCC).
Cite as

Joshua A. Grochow and Youming Qiao. On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{grochow_et_al:LIPIcs.ITCS.2021.31,
  author =	{Grochow, Joshua A. and Qiao, Youming},
  title =	{{On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.31},
  URN =		{urn:nbn:de:0030-drops-135702},
  doi =		{10.4230/LIPIcs.ITCS.2021.31},
  annote =	{Keywords: complexity class, tensor isomorphism, polynomial isomorphism, group isomorphism, stochastic local operations and classical communication}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.26
Improved Algorithms for Alternating Matrix Space Isometry: From Theory to Practice

Authors: Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
Motivated by testing isomorphism of p-groups, we study the alternating matrix space isometry problem (AltMatSpIso), which asks to decide whether two m-dimensional subspaces of n×n alternating (skew-symmetric if the field is not of characteristic 2) matrices are the same up to a change of basis. Over a finite field 𝔽_p with some prime p≠2, solving AltMatSpIso in time p^O(n+m) is equivalent to testing isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. The latter problem has long been considered a bottleneck case for the group isomorphism problem. Recently, Li and Qiao presented an average-case algorithm for AltMatSpIso in time p^O(n) when n and m are linearly related (FOCS '17). In this paper, we present an average-case algorithm for AltMatSpIso in time p^O(n+m). Besides removing the restriction on the relation between n and m, our algorithm is considerably simpler, and the average-case analysis is stronger. We then implement our algorithm, with suitable modifications, in Magma. Our experiments indicate that it improves significantly over default (brute-force) algorithms for this problem.
Cite as

Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson. Improved Algorithms for Alternating Matrix Space Isometry: From Theory to Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brooksbank_et_al:LIPIcs.ESA.2020.26,
  author =	{Brooksbank, Peter A. and Li, Yinan and Qiao, Youming and Wilson, James B.},
  title =	{{Improved Algorithms for Alternating Matrix Space Isometry: From Theory to Practice}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.26},
  URN =		{urn:nbn:de:0030-drops-128920},
  doi =		{10.4230/LIPIcs.ESA.2020.26},
  annote =	{Keywords: Alternating Matrix Spaces, Average-case Algorithm, p-groups of Class 2nd Exponent p, Magma}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.8
From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge Between Graphs and Alternating Matrix Spaces

Authors: Xiaohui Bei, Shiteng Chen, Ji Guan, Youming Qiao, and Xiaoming Sun

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
In the 1970’s, Lovász built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979). A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative rank problem (Garg-Gurvits-Oliveira-Wigderson, FOCS 2016; Ivanyos-Qiao-Subrahmanyam, ITCS 2017). In this paper, we lay the foundation for another bridge between graphs and alternating matrix spaces, in the context of independent sets and vertex colorings. The corresponding structures in alternating matrix spaces are isotropic spaces and isotropic decompositions, both useful structures in group theory and manifold theory. We first show that the maximum independent set problem and the vertex c-coloring problem reduce to the maximum isotropic space problem and the isotropic c-decomposition problem, respectively. Next, we show that several topics and results about independent sets and vertex colorings have natural correspondences for isotropic spaces and decompositions. These include algorithmic problems, such as the maximum independent set problem for bipartite graphs, and exact exponential-time algorithms for the chromatic number, as well as mathematical questions, such as the number of maximal independent sets, and the relation between the maximum degree and the chromatic number. These connections lead to new interactions between graph theory and algebra. Some results have concrete applications to group theory and manifold theory, and we initiate a variant of these structures in the context of quantum information theory. Finally, we propose several open questions for further exploration. (Dedicated to the memory of Ker-I Ko)
Cite as

Xiaohui Bei, Shiteng Chen, Ji Guan, Youming Qiao, and Xiaoming Sun. From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge Between Graphs and Alternating Matrix Spaces. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 8:1-8:48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bei_et_al:LIPIcs.ITCS.2020.8,
  author =	{Bei, Xiaohui and Chen, Shiteng and Guan, Ji and Qiao, Youming and Sun, Xiaoming},
  title =	{{From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge Between Graphs and Alternating Matrix Spaces}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{8:1--8:48},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.8},
  URN =		{urn:nbn:de:0030-drops-116932},
  doi =		{10.4230/LIPIcs.ITCS.2020.8},
  annote =	{Keywords: independent set, vertex coloring, graphs, matrix spaces, isotropic subspace}
}
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