@inproceedings{04fc8a5fcafd42c6b3f95466f7970b8b,
title = "Testing odd direct sums using high dimensional expanders",
abstract = "In this work, using methods from high dimensional expansion, we show that the property of k-direct-sum is testable for odd values of k . Previous work of [9] could inherently deal only with the case that k is even, using a reduction to linearity testing. Interestingly, our work is the first to combine the topological notion of high dimensional expansion (called co-systolic expansion) with the combinatorial/spectral notion of high dimensional expansion (called colorful expansion) to obtain the result. The classical k-direct-sum problem applies to the complete complex; Namely it considers a function defined over all k-subsets of some n sized universe. Our result here applies to any collection of k-subsets of an n-universe, assuming this collection of subsets forms a high dimensional expander.",
keywords = "Direct Sum, High Dimensional Expanders, Property Testing",
author = "Roy Gotlib and Tali Kaufman",
note = "Publisher Copyright: {\textcopyright} Roy Gotlib and Tali Kaufman.; 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019 ; Conference date: 20-09-2019 Through 22-09-2019",
year = "2019",
month = sep,
doi = "https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.50",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Dimitris Achlioptas and Vegh, {Laszlo A.}",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019",
address = "ألمانيا",
}