Directed Tree Decompositions

2014 ◽  
pp. 80-95
Author(s):  
Sebastian Kerkhoff ◽  
Friedrich Martin Schneider
Keyword(s):  
Directed Tree ◽  
Tree Decompositions

Odontopleura (Trilobita, Silurian), and a method of constrained congruency analysis

1990 ◽  
Vol 64 (4) ◽  
pp. 600-614 ◽  
Author(s):  
Jonathan M. Adrain ◽  
Brian D. E. Chatterton
Keyword(s):  
Cladistic Analysis ◽  
Canadian Arctic ◽  
Wide Distribution ◽  
Parsimony Analysis ◽  
Directed Tree ◽  
Shelf Slope ◽  
Major Species ◽  
Species Groups ◽  
The Universe ◽  
A New Species

Odontopleura (Odontopleura) arctica, a new species of odontopleurine trilobite, is described from the Canadian Arctic. A method of cladistic analysis is detailed. Parsimony analysis should be performed treating all characters as unordered. The universe of directed trees implied by the resulting rootless network(s) can then be examined and a preferred tree selected by a criterion of congruency. Namely, the most parsimonious directed tree that accommodates the most congruent arrangement of character-states should be taken as the preferred cladogram. Since this is essentially a general congruency method operating within the constraints of parsimony, it is termed “constrained congruency.” The method is applied to the genus Odontopleura, resulting in the recognition of two major species groups, the nominate subgenus and Sinespinaspis n. subgen. Odontopleura (Ivanopleura) dufrenoyi Barrande is tentatively included in the genus, but considered too poorly known for cladistic analysis. Species assigned to Odontopleura (Odontopleura) include Odontopleura ovata Emmrich, Odontopleura brevigena Chatterton and Perry, Odontopleura (Odontopleura) arctica n. sp., and Diacanthaspis serotina Apollonov. Species assigned to Sinespinaspis n. subgen. include Taemasaspis llandoveryana Šnajdr, Odontopleura greenwoodi Chatterton and Perry, Odontopleura maccallai Chatterton and Perry, and Odontopleura nehedensis Chatterton and Perry. Odontopleura bombini Chatterton and Perry is tentatively placed in synonymy with Odontopleura nehedensis. The genus had a wide distribution throughout the Early and Middle Silurian, due to preferences for deep-water, distal shelf or shelf-slope transition zone habitats.

Falsification of Hybrid Systems Using Adaptive Probabilistic Search

2021 ◽  
Vol 31 (3) ◽  
pp. 1-22
Author(s):  
Gidon Ernst ◽  
Sean Sedwards ◽  
Zhenya Zhang ◽  
Ichiro Hasuo
Keyword(s):  
Hybrid Systems ◽  
Input Signal ◽  
Tree Search ◽  
Single Trial ◽  
Decision Point ◽  
Directed Tree ◽  
Probabilistic Choice ◽  
Original Algorithm ◽  
Fine Grained ◽  
Probabilistic Search

We present and analyse an algorithm that quickly finds falsifying inputs for hybrid systems. Our method is based on a probabilistically directed tree search, whose distribution adapts to consider an increasingly fine-grained discretization of the input space. In experiments with standard benchmarks, our algorithm shows comparable or better performance to existing techniques, yet it does not build an explicit model of a system. Instead, at each decision point within a single trial, it makes an uninformed probabilistic choice between simple strategies to extend the input signal by means of exploration or exploitation. Key to our approach is the way input signal space is decomposed into levels, such that coarse segments are more probable than fine segments. We perform experiments to demonstrate how and why our approach works, finding that a fully randomized exploration strategy performs as well as our original algorithm that exploits robustness. We propose this strategy as a new baseline for falsification and conclude that more discriminative benchmarks are required.

AN IMPROVED ALGORITHM FOR FINDING TREE DECOMPOSITIONS OF SMALL WIDTH

2000 ◽  
Vol 11 (03) ◽  
pp. 365-371 ◽  
Author(s):  
LJUBOMIR PERKOVIĆ ◽  
BRUCE REED
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Tree Decomposition ◽  
Linear Time Algorithm ◽  
Input Graph ◽  
Primary Motivation ◽  
Small Width ◽  
Tree Decompositions ◽  
Improved Algorithm

We present a modification of Bodlaender's linear time algorithm that, for constant k, determine whether an input graph G has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k then a subgraph G′ of G of treewidth greater than k is returned along with a tree decomposition of G′ of width at most 2k. A consequence is that the fundamental disjoint rooted paths problem can now be solved in O(n2) time. This is the primary motivation of this paper.

scholarly journals Tree decompositions with small cost

2005 ◽  
Vol 145 (2) ◽  
pp. 143-154 ◽  
Author(s):  
Hans L. Bodlaender ◽  
Fedor V. Fomin
Keyword(s):  
Tree Decompositions

scholarly journals Distributed Function Computation Over a Rooted Directed Tree

2016 ◽  
Vol 62 (12) ◽  
pp. 7135-7152 ◽  
Author(s):  
Milad Sefidgaran ◽  
Aslan Tchamkerten
Keyword(s):  
Directed Tree ◽  
Function Computation ◽  
Distributed Function Computation

scholarly journals Two Short Proofs Concerning Tree-Decompositions

2002 ◽  
Vol 11 (6) ◽  
pp. 541-547 ◽  
Author(s):  
PATRICK BELLENBAUM ◽  
REINHARD DIESTEL
Keyword(s):  
Duality Theorem ◽  
Finite Graph ◽  
Tree Decomposition ◽  
Tree Width ◽  
Tree Decompositions

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.

Finding good tree decompositions by local search

2009 ◽  
Vol 32 ◽  
pp. 43-50 ◽  
Author(s):  
Stan van Hoesel ◽  
Bert Marchal
Keyword(s):  
Local Search ◽  
Tree Decompositions

Improving dynamic programming on tree decompositions

2015 ◽  
pp. 357-375
Author(s):  
Marek Cygan ◽  
Fedor V. Fomin ◽  
Łukasz Kowalik ◽  
Daniel Lokshtanov ◽  
Dániel Marx ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Tree Decompositions

scholarly journals Minimum size tree-decompositions

2018 ◽  
Vol 245 ◽  
pp. 109-127 ◽  
Author(s):  
Bi Li ◽  
Fatima Zahra Moataz ◽  
Nicolas Nisse ◽  
Karol Suchan
Keyword(s):  
Minimum Size ◽  
Tree Decompositions

Introducing Directed Tree Width

1999 ◽  
Vol 3 ◽  
pp. 222-229 ◽  
Author(s):  
B. Reed
Keyword(s):  
Directed Tree ◽  
Tree Width
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