5,508 research outputs found
Block Crossings in Storyline Visualizations
Storyline visualizations help visualize encounters of the characters in a
story over time. Each character is represented by an x-monotone curve that goes
from left to right. A meeting is represented by having the characters that
participate in the meeting run close together for some time. In order to keep
the visual complexity low, rather than just minimizing pairwise crossings of
curves, we propose to count block crossings, that is, pairs of intersecting
bundles of lines.
Our main results are as follows. We show that minimizing the number of block
crossings is NP-hard, and we develop, for meetings of bounded size, a
constant-factor approximation. We also present two fixed-parameter algorithms
and, for meetings of size 2, a greedy heuristic that we evaluate
experimentally.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Internal Pattern Matching Queries in a Text and Applications
We consider several types of internal queries: questions about subwords of a
text. As the main tool we develop an optimal data structure for the problem
called here internal pattern matching. This data structure provides
constant-time answers to queries about occurrences of one subword in
another subword of a given text, assuming that ,
which allows for a constant-space representation of all occurrences. This
problem can be viewed as a natural extension of the well-studied pattern
matching problem. The data structure has linear size and admits a linear-time
construction algorithm.
Using the solution to the internal pattern matching problem, we obtain very
efficient data structures answering queries about: primitivity of subwords,
periods of subwords, general substring compression, and cyclic equivalence of
two subwords. All these results improve upon the best previously known
counterparts. The linear construction time of our data structure also allows to
improve the algorithm for finding -subrepetitions in a text (a more
general version of maximal repetitions, also called runs). For any fixed
we obtain the first linear-time algorithm, which matches the linear
time complexity of the algorithm computing runs. Our data structure has already
been used as a part of the efficient solutions for subword suffix rank &
selection, as well as substring compression using Burrows-Wheeler transform
composed with run-length encoding.Comment: 31 pages, 9 figures; accepted to SODA 201
Generating Permutations with Restricted Containers
We investigate a generalization of stacks that we call
-machines. We show how this viewpoint rapidly leads to functional
equations for the classes of permutations that -machines generate,
and how these systems of functional equations can frequently be solved by
either the kernel method or, much more easily, by guessing and checking.
General results about the rationality, algebraicity, and the existence of
Wilfian formulas for some classes generated by -machines are
given. We also draw attention to some relatively small permutation classes
which, although we can generate thousands of terms of their enumerations, seem
to not have D-finite generating functions
Composable Constraint Models for Permutation Enumeration
Constraint programming (CP) is a powerful tool for modeling mathematical
concepts and objects and finding both solutions or counter examples. One of the
major strengths of CP is that problems can easily be combined or expanded. In
this paper, we illustrate that this versatility makes CP an ideal tool for
exploring problems in permutation patterns.
We declaratively define permutation properties, permutation pattern avoidance
and containment constraints using CP and show how this allows us to solve a
wide range of problems. We show how this approach enables the arbitrary
composition of these conditions, and also allows the easy addition of extra
conditions. We demonstrate the effectiveness of our techniques by modelling the
containment and avoidance of six permutation patterns, eight permutation
properties and measuring five statistics on the resulting permutations. In
addition to calculating properties and statistics for the generated
permutations, we show that arbitrary additional constraints can also be easily
and efficiently added.
This approach enables mathematicians to investigate permutation pattern
problems in a quick and efficient manner. We demonstrate the utility of
constraint programming for permutation patterns by showing how we can easily
and efficiently extend the known permutation counts for a conjecture involving
the class of 1324 avoiding permutations. For this problem, we expand the
enumeration of 1324-avoiding permutations with a fixed number of inversions to
permutations of length 16 and show for the first time that in the enumeration
there is a pattern occurring which follows a unique sequence on the Online
Encyclopedia of Integer Sequences
Smooth heaps and a dual view of self-adjusting data structures
We present a new connection between self-adjusting binary search trees (BSTs)
and heaps, two fundamental, extensively studied, and practically relevant
families of data structures. Roughly speaking, we map an arbitrary heap
algorithm within a natural model, to a corresponding BST algorithm with the
same cost on a dual sequence of operations (i.e. the same sequence with the
roles of time and key-space switched). This is the first general transformation
between the two families of data structures.
There is a rich theory of dynamic optimality for BSTs (i.e. the theory of
competitiveness between BST algorithms). The lack of an analogous theory for
heaps has been noted in the literature. Through our connection, we transfer all
instance-specific lower bounds known for BSTs to a general model of heaps,
initiating a theory of dynamic optimality for heaps.
On the algorithmic side, we obtain a new, simple and efficient heap
algorithm, which we call the smooth heap. We show the smooth heap to be the
heap-counterpart of Greedy, the BST algorithm with the strongest proven and
conjectured properties from the literature, widely believed to be
instance-optimal. Assuming the optimality of Greedy, the smooth heap is also
optimal within our model of heap algorithms. As corollaries of results known
for Greedy, we obtain instance-specific upper bounds for the smooth heap, with
applications in adaptive sorting.
Intriguingly, the smooth heap, although derived from a non-practical BST
algorithm, is simple and easy to implement (e.g. it stores no auxiliary data
besides the keys and tree pointers). It can be seen as a variation on the
popular pairing heap data structure, extending it with a "power-of-two-choices"
type of heuristic.Comment: Presented at STOC 2018, light revision, additional figure
An evaluation of genotyping by sequencing (GBS) to map the <em>Breviaristatum-e (ari-e)</em> locus in cultivated barley
ABSTRACT: We explored the use of genotyping by sequencing (GBS) on a recombinant inbred line population (GPMx) derived from a cross between the two-rowed barley cultivar ‘Golden Promise’ (ari-e.GP/Vrs1) and the six-rowed cultivar ‘Morex’ (Ari-e/vrs1) to map plant height. We identified three Quantitative Trait Loci (QTL), the first in a region encompassing the spike architecture gene Vrs1 on chromosome 2H, the second in an uncharacterised centromeric region on chromosome 3H, and the third in a region of chromosome 5H coinciding with the previously described dwarfing gene Breviaristatum-e (Ari-e). BACKGROUND: Barley cultivars in North-western Europe largely contain either of two dwarfing genes; Denso on chromosome 3H, a presumed ortholog of the rice green revolution gene OsSd1, or Breviaristatum-e (ari-e) on chromosome 5H. A recessive mutant allele of the latter gene, ari-e.GP, was introduced into cultivation via the cv. ‘Golden Promise’ that was a favourite of the Scottish malt whisky industry for many years and is still used in agriculture today. RESULTS: Using GBS mapping data and phenotypic measurements we show that ari-e.GP maps to a small genetic interval on chromosome 5H and that alternative alleles at a region encompassing Vrs1 on 2H along with a region on chromosome 3H also influence plant height. The location of Ari-e is supported by analysis of near-isogenic lines containing different ari-e alleles. We explored use of the GBS to populate the region with sequence contigs from the recently released physically and genetically integrated barley genome sequence assembly as a step towards Ari-e gene identification. CONCLUSIONS: GBS was an effective and relatively low-cost approach to rapidly construct a genetic map of the GPMx population that was suitable for genetic analysis of row type and height traits, allowing us to precisely position ari-e.GP on chromosome 5H. Mapping resolution was lower than we anticipated. We found the GBS data more complex to analyse than other data types but it did directly provide linked SNP markers for subsequent higher resolution genetic analysis
- …