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- research-articleAugust 2024
- research-articleMay 2024
Algebraic Global Gadgetry for Surjective Constraint Satisfaction
AbstractThe constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is an assignment to the variables satisfying all of the ...
- research-articleApril 2024
- research-articleMarch 2024
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- research-articleFebruary 2024
Bounds on depth of decision trees derived from decision rule systems with discrete attributes
Annals of Mathematics and Artificial Intelligence (KLU-AMAI), Volume 92, Issue 3Pages 703–732https://doi.org/10.1007/s10472-024-09933-xAbstractSystems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of ...
- research-articleDecember 2023
Beyond the Existential Theory of the Reals
Theory of Computing Systems (TOCSYS), Volume 68, Issue 2Pages 195–226https://doi.org/10.1007/s00224-023-10151-xAbstractWe show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness ...
- research-articleOctober 2023
- research-articleOctober 2023
Tractability of L 2-approximation and integration in weighted Hermite spaces of finite smoothness
AbstractIn this paper we consider integration and L 2-approximation for functions over R s from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature, which ...
- research-articleSeptember 2023
- research-articleJuly 2023
- research-articleJune 2023
Further -Complete Problems with PSD Matrix Factorizations
- research-articleMay 2023
- research-articleMay 2023
6-Uniform Maker-Breaker Game is PSPACE-Complete
AbstractIn a STOC 1976 paper, Schaefer proved that it is PSPACE-complete to determine the winner of the so-called Maker-Breaker game on a given set system, even when every set has size at most 11. Since then, there has been no improvement on this result. ...
- research-articleMay 2023
Maximum Cut on Interval Graphs of Interval Count Four is NP-Complete
Discrete & Computational Geometry (DCOG), Volume 71, Issue 3Pages 893–917https://doi.org/10.1007/s00454-023-00508-xAbstractThe computational complexity of the MaxCut problem restricted to interval graphs has been open since the 80’s, being one of the problems proposed by Johnson in his Ongoing Guide to NP-completeness, and has been settled as NP-complete only recently ...
- research-articleFebruary 2023
A simple and fast linear-time algorithm for divisor methods of apportionment
Mathematical Programming: Series A and B (MPRG), Volume 203, Issue 1-2Pages 187–205https://doi.org/10.1007/s10107-023-01929-5AbstractProportional apportionment is the problem of assigning seats to states (resp. parties) according to their relative share of the population (resp. votes), a field heavily influenced by the early work of Michel Balinski, not least his influential ...
- research-articleJanuary 2023