相关论文: Pure Parsimony Xor Haplotyping

Our main result is a full classification, for every connected graph $H$, of the computational complexity of Steiner Forest on $H$-subgraph-free graphs. To obtain this dichotomy, we establish the following new algorithmic, hardness, and…

A theory of numerical path-following in toric varieties was suggested in two previous papers. The motivation is solving systems of polynomials with real or complex coefficients. When those polynomials are not assumed 'dense', solving them…

We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type…

Given a signed permutation on $n$ elements, we need to sort it with the fewest reversals. This is a fundamental algorithmic problem motivated by applications in comparative genomics, as it allows to accurately model rearrangements in small…

Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…

We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…

We design an efficient algorithm that outputs tests for identifying predominantly homogeneous subcohorts of patients from large in-homogeneous datasets. Our theoretical contribution is a rounding technique, similar to that of Goemans and…

The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique…

In forensic genetics, short tandem repeats (STRs) are used for human identification (HID). Degraded biological trace samples with low amounts of short DNA fragments (low-quality DNA samples) pose a challenge for STR typing. Predefined…

In genetics it is often of interest to discover single nucleotide polymorphisms (SNPs) that are directly related to a disease, rather than just being associated with it. Few methods exist, however, addressing this so-called `true sparsity…

We present an extremely simple polynomial-space exponential-time $(1-\varepsilon)$-approximation algorithm for MAX-k-SAT that is (slightly) faster than the previous known polynomial-space $(1-\varepsilon)$-approximation algorithms by Hirsch…

Given two genomes with duplicate genes, \textsc{Zero Exemplar Distance} is the problem of deciding whether the two genomes can be reduced to the same genome without duplicate genes by deleting all but one copy of each gene in each genome.…

While linear mixed model (LMM) has shown a competitive performance in correcting spurious associations raised by population stratification, family structures, and cryptic relatedness, more challenges are still to be addressed regarding the…

We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…

The widely used genetic pleiotropic analysis of multiple phenotypes are often designed for examining the relationship between common variants and a few phenotypes. They are not suited for both high dimensional phenotypes and high…

We consider the problem of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$. We show that if $H$ admits a weak near unanimity polymorphism $\phi$ then deciding whether $G$ admits a homomorphism to $H$ (HOM($H$)) is…

Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…

Correspondence homomorphisms are both a generalization of standard homomorphisms and a generalization of correspondence colourings. For a fixed target graph $H$, the problem is to decide whether an input graph $G$, with each edge labeled by…

We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…

Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of…