scholarly journals Classifying Rotationally-Closed Languages Having Greedy Universal Cycles

10.37236/7932 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Joseph DiMuro
Keyword(s):  
Greedy Algorithm ◽  
Universal Cycles

Let $\textbf{T}(n,k)$ be the set of strings of length $n$ over the alphabet $\Sigma=\{1,2,\ldots,k\}$. A universal cycle for $\textbf{T}(n,k)$ can be constructed using a greedy algorithm: start with the string $k^n$, and continually append the least symbol possible without repeating a substring of length $n$. This construction also creates universal cycles for some subsets $\textbf{S}\subseteq\textbf{T}(n,k)$; we will classify all such subsets that are closed under rotations.

scholarly journals On a Greedy Algorithm to Construct Universal Cycles for Permutations

2019 ◽  
Vol 30 (01) ◽  
pp. 61-72
Author(s):  
Alice L. L. Gao ◽  
Sergey Kitaev ◽  
Wolfgang Steiner ◽  
Philip B. Zhang
Keyword(s):  
Greedy Algorithm ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Universal Cycles

A universal cycle for permutations of length [Formula: see text] is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length [Formula: see text], and containing all permutations of length [Formula: see text] as factors. It is well known that universal cycles for permutations of length [Formula: see text] exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length [Formula: see text], which is based on applying a greedy algorithm to a permutation of length [Formula: see text]. We prove that this approach gives a unique universal cycle [Formula: see text] for permutations, and we study properties of [Formula: see text].

scholarly journals Generalizing the Classic Greedy and Necklace Constructions of de Bruijn Sequences and Universal Cycles

10.37236/5517 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Joe Sawada ◽  
Aaron Williams ◽  
Dennis Wong
Keyword(s):  
Greedy Algorithm ◽  
Interesting Property ◽  
Universal Cycles ◽  
De Bruijn Sequences ◽  
Lyndon Word ◽  
De Bruijn

We present a class of languages that have an interesting property: For each language $\mathbf{L}$ in the class, both the classic greedy algorithm and the classic Lyndon word (or necklace) concatenation algorithm provide the lexicographically smallest universal cycle for $\mathbf{L}$. The languages consist of length $n$ strings over $\{1,2,\ldots ,k\}$ that are closed under rotation with their subset of necklaces also being closed under replacing any suffix of length $i$ by $i$ copies of $k$. Examples include all strings (in which case universal cycles are commonly known as de Bruijn sequences), strings that sum to at least $s$, strings with at most $d$ cyclic descents for a fixed $d>0$, strings with at most $d$ cyclic decrements for a fixed $d>0$, and strings avoiding a given period. Our class is also closed under both union and intersection, and our results generalize results of several previous papers.

Implementasi Algoritma Dijkstra Pada Game Pacman

CCIT Journal ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 170-176
Author(s):  
Anggit Dwi Hartanto ◽  
Aji Surya Mandala ◽  
Dimas Rio P.L. ◽  
Sidiq Aminudin ◽  
Andika Yudirianto
Keyword(s):  
Artificial Intelligence ◽  
Greedy Algorithm ◽  
Dijkstra Algorithm ◽  
Testing Phase ◽  
A Value ◽  
Route Problem ◽  
Starting Point ◽  
The Greedy Algorithm

Pacman is one of the labyrinth-shaped games where this game has used artificial intelligence, artificial intelligence is composed of several algorithms that are inserted in the program and Implementation of the dijkstra algorithm as a method of solving problems that is a minimum route problem on ghost pacman, where ghost plays a role chase player. The dijkstra algorithm uses a principle similar to the greedy algorithm where it starts from the first point and the next point is connected to get to the destination, how to compare numbers starting from the starting point and then see the next node if connected then matches one path with the path). From the results of the testing phase, it was found that the dijkstra algorithm is quite good at solving the minimum route solution to pursue the player, namely by getting a value of 13 according to manual calculations

Parallelism of adaptive Hungary greedy algorithm for biomolecular networks alignment

2013 ◽  
Vol 33 (12) ◽  
pp. 3321-3325
Author(s):  
Jin MA ◽  
Jiang XIE ◽  
Dongbo DAI ◽  
Jun TAN ◽  
Wu ZHANG
Keyword(s):  
Greedy Algorithm ◽  
Biomolecular Networks
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