scholarly journals Subexponential algorithms for variants of the homomorphism problem in string graphs

2020 ◽  
Vol 109 ◽  
pp. 126-144 ◽  
Author(s):  
Karolina Okrasa ◽  
Paweł Rzążewski
Keyword(s):  
String Graphs ◽  
Subexponential Algorithms

scholarly journals Conflict-Free Coloring of String Graphs

2020 ◽  
Author(s):  
Chaya Keller ◽  
Alexandre Rok ◽  
Shakhar Smorodinsky
Keyword(s):  
String Graphs

scholarly journals Bit-parallel sequence-to-graph alignment

2019 ◽  
Vol 35 (19) ◽  
pp. 3599-3607 ◽  
Author(s):  
Mikko Rautiainen ◽  
Veli Mäkinen ◽  
Tobias Marschall
Keyword(s):  
Variant Calling ◽  
Supplementary Information ◽  
Global Alignment ◽  
Alignment Algorithm ◽  
Exact Matching ◽  
Worst Case ◽  
De Bruijn Graphs ◽  
Graph Alignment ◽  
Linear Sequence ◽  
String Graphs

Abstract Motivation Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence the genetic variation present in a population. Being able to align sequencing reads to such graphs is a key step for many analyses and its applications include genome assembly, read error correction and variant calling with respect to a variation graph. Results We generalize two linear sequence-to-sequence algorithms to graphs: the Shift-And algorithm for exact matching and Myers’ bitvector algorithm for semi-global alignment. These linear algorithms are both based on processing w sequence characters with a constant number of operations, where w is the word size of the machine (commonly 64), and achieve a speedup of up to w over naive algorithms. For a graph with |V| nodes and |E| edges and a sequence of length m, our bitvector-based graph alignment algorithm reaches a worst case runtime of O(|V|+⌈mw⌉|E| log w) for acyclic graphs and O(|V|+m|E| log w) for arbitrary cyclic graphs. We apply it to five different types of graphs and observe a speedup between 3-fold and 20-fold compared with a previous (asymptotically optimal) alignment algorithm. Availability and implementation https://github.com/maickrau/GraphAligner Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Subexponential Algorithms for Class Group and Unit Computations

1997 ◽  
Vol 24 (3-4) ◽  
pp. 433-441 ◽  
Author(s):  
H. COHEN ◽  
F. DIAZ Y DIAZ ◽  
M. OLIVIER
Keyword(s):  
Class Group ◽  
Subexponential Algorithms

scholarly journals A Separator Theorem for String Graphs and its Applications

2009 ◽  
Vol 19 (3) ◽  
pp. 371-390 ◽  
Author(s):  
JACOB FOX ◽  
JÁNOS PACH
Keyword(s):  
Intersection Graph ◽  
Equal Size ◽  
Bipartite Subgraph ◽  
String Graphs ◽  
String Graph ◽  
Complete Bipartite Subgraph ◽  
Labelled Trees ◽  
Separator Theorem ◽  
Labelled Graphs

A string graph is the intersection graph of a collection of continuous arcs in the plane. We show that any string graph with m edges can be separated into two parts of roughly equal size by the removal of $O(m^{3/4}\sqrt{\log m})$ vertices. This result is then used to deduce that every string graph with n vertices and no complete bipartite subgraph Kt,t has at most ctn edges, where ct is a constant depending only on t. Another application shows that locally tree-like string graphs are globally tree-like: for any ε > 0, there is an integer g(ε) such that every string graph with n vertices and girth at least g(ε) has at most (1 + ε)n edges. Furthermore, the number of such labelled graphs is at most (1 + ε)nT(n), where T(n) = nn−2 is the number of labelled trees on n vertices.

scholarly journals Constructing String Graphs in External Memory

2014 ◽  
pp. 311-325 ◽  
Author(s):  
Paola Bonizzoni ◽  
Gianluca Della Vedova ◽  
Yuri Pirola ◽  
Marco Previtali ◽  
Raffaella Rizzi
Keyword(s):  
External Memory ◽  
String Graphs
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