Related papers: Genomic Problems Involving Copy Number Profiles: C…
Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
Genomic copy number variation (CNV) is a large source of variation between organisms, and its consequences include phenotypic differences and genetic disorders. CNVs are commonly detected by hybridizing genomic DNA to microarrays of nucleic…
A major challenge in next-generation genome sequencing (NGS) is to assemble massive overlapping short reads that are randomly sampled from DNA fragments. To complete assembling, one needs to finish a fundamental task in many leading…
We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…
A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such…
The 0/1 knapsack problem is weakly NP-hard in that there exist pseudo-polynomial time algorithms based on dynamic programming that can solve it exactly. There are also the core branch and bound algorithms that can solve large randomly…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Detecting critical nodes in sparse graphs is important in a variety of application domains, such as network vulnerability assessment, epidemic control, and drug design. The critical node problem (CNP) aims to find a set of critical nodes…
Covering alignment problems arise from recent developments in genomics; so called pan-genome graphs are replacing reference genomes, and advances in haplotyping enable full content of diploid genomes to be used as basis of sequence…
In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings.…
Motivated by the study of genome rearrangements, the NP-hard Minimum Common String Partition problems asks, given two strings, to split both strings into an identical set of blocks. We consider an extension of this problem to unbalanced…
The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint…
The Exact Circular Pattern Matching (ECPM) problem consists of reporting every occurrence of a rotation of a pattern $P$ in a text $T$. In many real-world applications, specifically in computational biology, circular rotations are of…
The edit distance under the DCJ model can be computed in linear time for genomes with equal content or with Indels. But it becomes NP-Hard in the presence of duplications, a problem largely unsolved especially when Indels are considered. In…
Neural network compression empowers the effective yet unwieldy deep convolutional neural networks (CNN) to be deployed in resource-constrained scenarios. Most state-of-the-art approaches prune the model in filter-level according to the…
DNA Copy number variation (CNV) has recently gained considerable interest as a source of genetic variation that likely influences phenotypic differences. Many statistical and computational methods have been proposed and applied to detect…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems…
One of the main challenges in Computational Biology is to find the evolutionary distance between two organisms. In the field of comparative genomics, one way to estimate such distance is to find a minimum cost sequence of rearrangements…