Related papers: Time and Space Efficient Algorithms for RNA Foldin…
Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU-base pairings (secondary structure) and additional cross-serial base pairs. These…
The closest pair problem is a fundamental problem of computational geometry: given a set of $n$ points in a $d$-dimensional space, find a pair with the smallest distance. A classical algorithm taught in introductory courses solves this…
Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be…
Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a…
We revisit Hopcroft's problem and related fundamental problems about geometric range searching. Given $n$ points and $n$ lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line…
Subset-Sum is an NP-complete problem where one must decide if a multiset of $n$ integers contains a subset whose elements sum to a target value $m$. The best-known classical and quantum algorithms run in time $\tilde{O}(2^{n/2})$ and…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…
The Ribonucleic Acid (RNA) inverse folding problem, designing nucleotide sequences that fold into specific tertiary structures, is a fundamental computational biology problem with important applications in synthetic biology and…
A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=\lceil \log_2N\rceil$-qubit state. It has been proven that any algorithm universally implementing this…
We show that there is a polynomial space algorithm that counts the number of perfect matchings in an $n$-vertex graph in $O^*(2^{n/2})\subset O(1.415^n)$ time. ($O^*(f(n))$ suppresses functions polylogarithmic in $f(n)$).The previously…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
Sequence partition problems arise in many fields, such as sequential data analysis, information transmission, and parallel computing. In this paper, we study the following partition problem variant: given a sequence of $n$ items…
In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
This paper develops a new technique for proving amortized, randomized cell-probe lower bounds on dynamic data structure problems. We introduce a new randomized nondeterministic four-party communication model that enables "accelerated",…
Many ncRNAs function through RNA-RNA interactions. Fast and reliable RNA structure prediction with consideration of RNA-RNA interaction is useful. Some existing tools are less accurate due to omitting the competing of intermolecular and…
Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. To tackle…
The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…
We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…