Related papers: Minimum length RNA folding trajectories
In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called $n$-fold integer programming. An $n$-fold integer program (IP) has a highly uniform…
Graphs have become a key tool when modeling and solving problems in different areas. The Floyd-Warshall (FW) algorithm computes the shortest path between all pairs of vertices in a graph and is employed in areas like communication…
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
Background: In the Nearest-Neighbor Thermodynamic Model, a standard approach for RNA secondary structure prediction, the energy of the multiloops is modeled using a linear entropic penalty governed by three branching parameters. Although…
Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…
Minimum flow decomposition (MFD) is the strongly NP-hard problem of finding a smallest set of integer weighted $s$-$t$ paths in an $s$-$t$ DAG $G$ whose weighted sum is equal to a given flow $f$ on $G$. Despite its many practical…
Given a graph and two fixed vertices $s$ and $t$, the Replacement Path Problem (RP) is to compute for every edge $e$, the distance between $s$ and $t$ when $e$ is removed. There are two natural extensions to RP: (1) Single Source…
Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and…
The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…
In a geometric network G = (S, E), the graph distance between two vertices u, v in S is the length of the shortest path in G connecting u to v. The dilation of G is the maximum factor by which the graph distance of a pair of vertices…
We formulate the RNA folding problem as an $N\times N$ matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is…
Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
Given an undirected graph and two disjoint vertex pairs $s_1,t_1$ and $s_2,t_2$, the Shortest two disjoint paths problem (S2DP) asks for the minimum total length of two vertex disjoint paths connecting $s_1$ with $t_1$, and $s_2$ with…
Computational prediction of RNA structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence,…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the…
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray…
In this paper, we discuss the maximum flow problem in the two-party communication model, where two parties, each holding a subset of edges on a common vertex set, aim to compute the maximum flow of the union graph with minimal…