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A popular method in combinatorial optimization is to express polytopes P, which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constraints down to a…
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…
Good representations for phylogenetic trees and networks are important for optimizing storage efficiency and implementation of scalable methods for the inference and analysis of evolutionary trees for genes, genomes and species. We…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…
A proper vertex of a rooted tree with totally ordered vertices is a vertex that is less than all its proper descendants. We count several kinds of labeled rooted trees and forests by the number of proper vertices. Our results are all…
We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e a…
The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present two novel stochastic algorithms, which we call the junction-tree expander and junction-tree collapser…
Phylogenetic trees summarize evolutionary relationships between organisms, and tools to analyze collections of phylogenetic trees enable contrasts between different genes' ancestry. The BHV metric space has enabled the analysis of…
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula $F$, 1) It is NP-hard to find a CP refutation of $F$ in time polynomial in the length of the shortest such refutation; and 2)unless Gap-Hitting-Set…
The Hausdorff distance is a relatively new measure of similarity of graphs. The notion of the Hausdorff distance considers a special kind of a common subgraph of the compared graphs and depends on the structural properties outside of the…
We exactly determine the maximum possible hook length of $(s,t)$-core partitions with $d$-distinct parts when there are finitely many such partitions. Moreover, we provide an algorithm to construct a $d$-distinct $(s,t)$-core partition with…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
In this letter we describe the pseudoparticle multipole method (P2M2), a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the…
Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes,…
Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find…
When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…