Improving the Predicting Power of Partial Order Based QSARs through Linear Extensions

2002 ◽  
Vol 42 (4) ◽  
pp. 806-811 ◽  
Author(s):  
Lars Carlsen ◽  
Dorte B. Lerche ◽  
Peter B. Sørensen
Keyword(s):  
Partial Order ◽  
Linear Extensions

Ranking of chemical substances based on the Japanese Pollutant Release and Transfer Register using partial order theory and random linear extensions

Chemosphere ◽  
2004 ◽  
Vol 55 (7) ◽  
pp. 1005-1025 ◽  
Author(s):  
Dorte Lerche ◽  
Sanae Y. Matsuzaki ◽  
Peter B. Sørensen ◽  
Lars Carlsen ◽  
Ole John Nielsen
Keyword(s):  
Partial Order ◽  
Order Theory ◽  
Linear Extensions ◽  
Chemical Substances

Comparison of the combined monitoring-based and modelling-based priority setting scheme with partial order theory and random linear extensions for ranking of chemical substances

Chemosphere ◽  
2002 ◽  
Vol 49 (6) ◽  
pp. 637-649 ◽  
Author(s):  
Dorte Lerche ◽  
Peter B. Sørensen ◽  
Henrik Sørensen Larsen ◽  
Lars Carlsen ◽  
Ole John Nielsen
Keyword(s):  
Partial Order ◽  
Priority Setting ◽  
Order Theory ◽  
Linear Extensions ◽  
Chemical Substances

scholarly journals Graph Orientations and Linear Extensions.

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Benjamin Iriarte
Keyword(s):  
Partial Order ◽  
Simple Graph ◽  
Linear Extensions ◽  
Acyclic Orientations ◽  
International Audience ◽  
General Graphs ◽  
Odd Cycles

International audience Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph, and therefore we can count the number of linear extensions of these posets. We want to know which choice of orientation maximizes the number of linear extensions of the corresponding poset, and this problem is solved essentially for comparability graphs and odd cycles, presenting several proofs. We then provide an inequality for general graphs and discuss further techniques.

scholarly journals On the dimension of vertex labeling of $k$-uniform dcsl of $k$-uniform caterpillar

2016 ◽  
Vol 8 (1) ◽  
pp. 134-149
Author(s):  
K. Nageswara Rao ◽  
K.A. Germina ◽  
P. Shaini
Keyword(s):  
Partial Order ◽  
Connected Graph ◽  
Linear Order ◽  
Linear Extension ◽  
Linear Extensions ◽  
Path Distance ◽  
Minimum Number

A distance compatible set labeling (dcsl) of a connected graph $G$ is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a nonempty ground set, such that the corresponding induced function $f^{\oplus} :E(G) \rightarrow 2^{X}\setminus \{\emptyset\}$ given by $f^{\oplus}(uv)= f(u)\oplus f(v)$ satisfies $\mid f^{\oplus}(uv) \mid = k_{(u,v)}^{f}d_{G}(u,v) $ for every pair of distinct vertices $u, v \in V(G),$ where $d_{G}(u,v)$ denotes the path distance between $u$ and $v$ and $k_{(u,v)}^{f}$ is a constant, not necessarily an integer. A dcsl $f$ of $G$ is $k$-uniform if all the constant of proportionality with respect to $f$ are equal to $k,$ and if $G$ admits such a dcsl then $G$ is called a $k$-uniform dcsl graph. The $k$-uniform dcsl index of a graph $G,$ denoted by $\delta_{k}(G)$ is the minimum of the cardinalities of $X,$ as $X$ varies over all $k$-uniform dcsl-sets of $G.$ A linear extension ${\mathbf{L}}$ of a partial order ${\mathbf{P}} = (P, \preceq)$ is a linear order on the elements of $P$, such that $ x \preceq y$ in ${\mathbf{P}}$ implies $ x \preceq y$ in ${\mathbf{L}}$, for all $x, y \in P$. The dimension of a poset ${\mathbf{P}},$ denoted by $dim({\mathbf{P}}),$ is the minimum number of linear extensions on ${\mathbf{P}}$ whose intersection is `$\preceq$'. In this paper we prove that $dim({\mathcal{F}}) \leq \delta_{k}(P^{+k}_n),$ where ${\mathcal{F}}$ is the range of a $k$-uniform dcsl of the $k$-uniform caterpillar, denoted by $P^{+k}_n \ (n\geq 1, k\geq 1)$ on `$n(k+1)$' vertices.

scholarly journals The average number of linear extensions of a partial order

1996 ◽  
Vol 73 (2) ◽  
pp. 193-206 ◽  
Author(s):  
Graham Brightwell ◽  
Hans Jürgen Prömel ◽  
Angelika Steger
Keyword(s):  
Partial Order ◽  
Linear Extensions

scholarly journals Linear Extensions of a Random Partial Order

1994 ◽  
Vol 4 (1) ◽  
pp. 108-123 ◽  
Author(s):  
Noga Alon ◽  
Bela Bollobas ◽  
Graham Brightwell ◽  
Svante Janson
Keyword(s):  
Partial Order ◽  
Linear Extensions

scholarly journals A Scalable Scheme for Counting Linear Extensions

2018 ◽  
Author(s):  
Topi Talvitie ◽  
Kustaa Kangas ◽  
Teppo Niinimäki ◽  
Mikko Koivisto
Keyword(s):  
Artificial Intelligence ◽  
Partial Order ◽  
Polynomial Time ◽  
State Of The Art ◽  
Hard Problem ◽  
Approximate Counting ◽  
Linear Extensions ◽  
Exponential Time ◽  
Running Time ◽  
Cnf Formulas

Counting the linear extensions of a given partial order not only has several applications in artificial intelligence but also represents a hard problem that challenges modern paradigms for approximate counting. Recently, Talvitie et al. (AAAI 2018) showed that an exponential time scheme beats the fastest known polynomial time schemes in practice, even if allowing hours of running time. Here, we present a novel scheme, relaxation Tootsie Pop, which in our experiments exhibits polynomial characteristics and significantly outperforms previous schemes. We also instantiate state-of-the-art model counters for CNF formulas; two natural encodings yield schemes that, however, are inferior to the more specialized schemes.

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