minor updates

Author: bsubercaseaux

_bibliography/papers.bib

@@ -434,3 +434,85 @@ @article{mackey2024pentagonminimizationcomputation
       bibtex_show = {true}
 }
 
+
+@inproceedings{subercaseauxFormalVerificationEmpty2024,
+  title = {Formal {{Verification}} of the {{Empty Hexagon Number}}},
+  booktitle = {15th {{International Conference}} on {{Interactive Theorem Proving}} ({{ITP}} 2024)},
+  author = {Subercaseaux, Bernardo and Nawrocki, Wojciech and Gallicchio, James and Codel, Cayden and Carneiro, Mario and Heule, Marijn J. H.},
+  editor = {Bertot, Yves and Kutsia, Temur and Norrish, Michael},
+  year = 2024,
+  series = {Leibniz {{International Proceedings}} in {{Informatics}} ({{LIPIcs}})},
+  volume = {309},
+  pages = {35:1--35:19},
+  publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f\"ur Informatik},
+  address = {Dagstuhl, Germany},
+  issn = {1868-8969},
+  doi = {10.4230/LIPIcs.ITP.2024.35},
+  urldate = {2025-05-14},
+  isbn = {978-3-95977-337-9},
+  keywords = {Discrete Computational Geometry,Empty Hexagon Number,Erd\Hos-Szekeres},
+  selected = {true},
+  bibtex_show = {true},
+  pdf={https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.35/LIPIcs.ITP.2024.35.pdf}
+}
+
+
+@inproceedings{subercaseauxAutomatedSymmetricConstructions2026,
+  title = {Automated {{Symmetric Constructions}} in {{Discrete Geometry}}},
+  booktitle = {Intelligent {{Computer Mathematics}}},
+  author = {Subercaseaux, Bernardo and Mackey, Ethan and Qian, Long and Heule, Marijn},
+  editor = {{de Paiva}, Valeria and Koepke, Peter},
+  year = 2026,
+  pages = {29--47},
+  publisher = {Springer Nature Switzerland},
+  address = {Cham},
+  abstract = {We present a computational methodology for obtaining rotationally symmetric sets of points satisfying discrete geometric constraints, and demonstrate its applicability by discovering new solutions to some well-known problems in combinatorial geometry. Our approach takes the usage of SAT solvers in discrete geometry further by directly embedding rotational symmetry into the combinatorial encoding of geometric configurations. Then, to realize concrete point sets corresponding to abstract designs provided by a SAT solver, we introduce a novel local-search realizability solver, which shows excellent practical performance despite the intrinsic \$\$\textbackslash exists \textbackslash mathbb \textbraceleft R\textbraceright\$\${$\exists$}R-completeness of the problem. Leveraging this combined approach, we provide symmetric extremal solutions to the Erd\H os-Szekeres problem, as well as a minimal odd-sized solution with 21 points for the everywhere-unbalanced-points problem, improving on the previously known 23-point configuration. The imposed symmetries yield more aesthetically appealing solutions, enhancing human interpretability, and simultaneously offer computational benefits by significantly reducing the number of variables required to encode discrete geometric problems.},
+  isbn = {978-3-032-07021-0},
+  selected = {true},
+  bibtex_show = {true},
+  pdf={https://arxiv.org/pdf/2506.00224}
+}
+
+
+@inproceedings{subercaseauxUnfoldingBoxesLocalConstraints2025,
+  author = {Qian, Long and Wang, Eric and Subercaseaux, Bernardo and Heule, Marijn J. H.},
+  title = {https://arxiv.org/pdf/2506.01079},
+  year = {2025},
+  isbn = {978-3-031-99983-3},
+  publisher = {Springer-Verlag},
+  address = {Berlin, Heidelberg},
+  url = {https://doi.org/10.1007/978-3-031-99984-0_38},
+  doi = {10.1007/978-3-031-99984-0_38},
+  abstract = {We consider the problem of finding and enumerating polyominos that can be folded into multiple non-isomorphic boxes. While several computational approaches have been proposed, including SAT, randomized algorithms, and decision diagrams, none has been able to perform at scale. We argue that existing SAT encodings are hindered by the presence of global constraints (e.g., graph connectivity or acyclicity), which are generally hard to encode effectively and hard for solvers to reason about. In this work, we propose a new SAT-based approach that replaces these global constraints with simple local constraints that have substantially better propagation properties. Our approach dramatically improves the scalability of both computing and enumerating common box unfoldings: (i) while previous approaches could only find common unfoldings of two boxes up to area 88, ours easily scales beyond 150, and (ii) while previous approaches were only able to enumerate common unfoldings up to area 30, ours scales up to 60. This allows us to rule out 46, 54, and 58 as the smallest areas allowing a common unfolding of three boxes, thereby refuting a conjecture of Xu et al. (2017).},
+  booktitle = {Automated Deduction – CADE 30: 30th International Conference on Automated Deduction, Stuttgart, Germany, July 28-31, 2025, Proceedings},
+  pages = {736–754},
+  numpages = {19},
+  keywords = {Box folding, SAT encodings, Graph connectivity, Graph cyclicity, Local constraints},
+  location = {Stuttgart, Germany},
+  selected = {true},
+  bibtex_show = {true},
+  pdf = {https://arxiv.org/pdf/2506.01079}
+}
+
+
+@article{subercaseauxExplainingKNearest2025,
+  author = {Barcel\'{o}, Pablo and Kozachinskiy, Alexander and Romero, Miguel and Subsercaseaux, Bernardo and Verschae, Jos\'{e}},
+  title = {Explaining k-Nearest Neighbors: Abductive and Counterfactual Explanations},
+  year = {2025},
+  issue_date = {May 2025},
+  publisher = {Association for Computing Machinery},
+  address = {New York, NY, USA},
+  volume = {3},
+  number = {2},
+  url = {https://doi.org/10.1145/3725234},
+  doi = {10.1145/3725234},
+  abstract = {Despite the wide use of k-Nearest Neighbors as classification models, their explainability properties remain poorly understood from a theoretical perspective. While nearest neighbors classifiers offer interpretability from a ''data perspective'', in which the classification of an input vector x is explained by identifying the vectors v1, ..., vk in the training set that determine the classification of x, we argue that such explanations can be impractical in high-dimensional applications, where each vector has hundreds or thousands of features and it is not clear what their relative importance is. Hence, we focus on understanding nearest neighbor classifications through a ''feature perspective'', in which the goal is to identify how the values of the features in x affect its classification. Concretely, we study abductive explanations such as ''minimum sufficient reasons'', which correspond to sets of features in x that are enough to guarantee its classification, and counterfactual explanations based on the minimum distance feature changes one would have to perform in x to change its classification. We present a detailed landscape of positive and negative complexity results for counterfactual and abductive explanations, distinguishing between discrete and continuous feature spaces, and considering the impact of the choice of distance function involved. Finally, we show that despite some negative complexity results, Integer Quadratic Programming and SAT solving allow for computing explanations in practice.},
+  journal = {Proc. ACM Manag. Data},
+  month = jun,
+  articleno = {97},
+  numpages = {26},
+  keywords = {XAI, explainability, interpretability, nearest neighbors},
+  selected = {true},
+  bibtex_show = {true},
+  pdf = {https://arxiv.org/pdf/2501.06078}
+}

_pages/publications.md

@@ -10,12 +10,12 @@ nav: true
 My most up-to-date list of papers is usually on [Google Scholar](https://scholar.google.com/citations?user=0EOonpYAAAAJ&hl=en), but here you can find some summarized data as well as my best attempt to have an updated and tidy list, with bibtex references, abstracts, and links to download.
 
 ## Summarized Data
-1. **h-index**: 8
+1. **h-index**: 10
 2. **Erdős number**: 3 (e.g., me → Daniel Lokshtanov → Noga Alon → Paul Erdős).
-3. **Collaborators from**: Chile, China, France, India, Netherlands, Norway, Portugal, Russia, Spain, USA. [^2]
-4. **Most common conference**: NeurIPS (5 papers there).
+3. **Collaborators from**: Austria, Chile, China, Germany, France, Japan, India, Netherlands, Norway, Portugal, Russia, Slovakia, Spain, USA. 
+4. **Most common conference**: NeurIPS (5 papers there). Actively trying to change this 🙃.
 5. **Most fun conference**: <a href="https://sites.google.com/view/fun2022/home?pli=1">FUN with algorithms.</a>
-6. **Distinctions**: Distinguished paper award, PODS'2025. Runner-up for Best paper award at CICM'2024, Best paper award at LPAR'2023. Best paper award nomination at TACAS'2023.  Spotlight paper at NeurIPS'2021, and spotlight paper at <a href="https://www.afciworkshop.org/afci-2020/home">AFCI@NeurIPS'2020 workshop</a>. 1st place in Latin American Contest of Master theses in Artificial Intelligence IEEE LA-CCI.
+6. **Distinctions**: Best paper award at CICM'2025, Distinguished paper award, PODS'2025. Runner-up for Best paper award at CICM'2024, Best paper award at LPAR'2023. Best paper award nomination at TACAS'2023.  Spotlight paper at NeurIPS'2021, and spotlight paper at <a href="https://www.afciworkshop.org/afci-2020/home">AFCI@NeurIPS'2020 workshop</a>. 1st place in Latin American Contest of Master theses in Artificial Intelligence IEEE LA-CCI.
 
 
 ## Attempt of an Updated List of Papers
@@ -26,4 +26,3 @@ My most up-to-date list of papers is usually on [Google Scholar](https://scholar
 </div>
 
 [^1]: This count might include a journal version of a conference paper separately, if there's a enough difference between the two.
-[^2]: I am hoping to work with people from even more countries!

_posts/2025-05-09-subquadratic.md

@@ -24,9 +24,13 @@ While cardinality constraints are known to admit compact encodings with $$\mathc
  $$\mathcal{O}(a + b) = \mathcal{O}(|V(K_{a, b})|)$$
   many clauses, instead of the $$a \cdot b$$ used by Equation 1. Moreover, equivalence can be seen directly by resolving over $$s_A$$ and $$s_B$$.
 
-**Biclique Coverings.** Suppose now $$G$$ is an arbitrary graph again, but we have a set of bicliques $$B_1, \ldots, B_r$$, with $$V(B_i) \subseteq V(G)$$ for each $$1 \leq i \leq r$$, and such that $$\bigcup_{i=1}^r E(B_i) = E(G)$$. Such a set of bicliques is said to be a _``biclique covering''_ of $$G$$. Then, for any set $$S \subseteq V(G)$$, we trivially have that $$S$$ is an independent set of $$G$$ if and only if $$S \cap V(B_i)$$ is an independent set of $$B_i$$ for every $$1 \leq i \leq r$$. Now, applying the method of the previous paragraph for each $$B_i$$ yields an encoding using $$\mathcal{O}(\sum_{i=1}^r |V(B_i)|)$$ many clauses. Fortunately, [a classic result of Chung, Erdős, and Spencer](https://users.renyi.hu/~p_erdos/1983-20.pdf) says that for any $G$ there is a biclique covering such that
+**Biclique Coverings.** Suppose now $$G$$ is an arbitrary graph again, but we have a set of bicliques $$B_1, \ldots, B_r$$, with $$V(B_i) \subseteq V(G)$$ for each $$1 \leq i \leq r$$, and such that $$\bigcup_{i=1}^r E(B_i) = E(G)$$. Such a set of bicliques is said to be a _``biclique covering''_ of $$G$$. Then, for any set $$S \subseteq V(G)$$, we trivially have that $$S$$ is an independent set of $$G$$ if and only if $$S \cap V(B_i)$$ is an independent set of $$B_i$$ for every $$1 \leq i \leq r$$. Now, applying the method of the previous paragraph for each $$B_i$$ yields an encoding using $$\mathcal{O}(\sum_{i=1}^r |V(B_i)|)$$ many clauses. Fortunately, [a classic result of Chung, Erdős, and Spencer](https://users.renyi.hu/~p_erdos/1983-20.pdf) says that for any $$G$$ there is a biclique covering such that
  $$
  \sum_{i=1}^r |V(B_i)| \in \mathcal{O}(|V(G)|^2 / \lg (|V(G)|)).
  $$
  Furthermore, Mubayi and Turán proved that such a covering can be computed in polynomial time [[3]](https://arxiv.org/pdf/0905.2527), which allows therefore to construct the succinct encoding from an input graph in polynomial time. Naturally, without this runtime restriction the result of this note would be trivial, since one could first solve the independent set instance and then build a constant-size formula according to the answer.
- 
+ 
+
+ ## Edit from a few months later:
+
+ I have written more in depth about this result here: https://arxiv.org/abs/2506.14042. But more importantly, together with Andrew Krapivin, Benjamin Pzybocki, and Nicolás Sanhueza-Matamala, we have improved the best bounds on biclique partitions/coverings for graphs, optimally solved the hypergraph case as well, and significantly improved the algorithmic aspects of the problem since Mubayi and Turán's result. The paper is available here: https://www.arxiv.org/abs/2511.11855.