How to Systematically Embed Cycles in Balanced Hypercubes

2017 ◽  
Vol 5 (1) ◽  
pp. 44-56
Author(s):  
Hsuan-Han Chang ◽  
Kuan-Ting Chen ◽  
Pao-Lien Lai
Keyword(s):  
Parallel Algorithms ◽  
Distributed Memory ◽  
Linear Time ◽  
Time Algorithm ◽  
Parallel Computers ◽  
Hamiltonian Cycles ◽  
Linear Time Algorithm ◽  
Systematic Method ◽  
Balanced Hypercube ◽  
Host Graph

The balanced hypercube is a variant of the hypercube structure and has desirable properties like connectivity, regularity, and symmetry. The cycle is a popular interconnection topology and has been widely used in distributed-memory parallel computers. Moreover, parallel algorithms of cycles have been extensively developed and used. The problem of how to embed cycles into a host graph has attracted a great attention in recent years. However, there is no systematic method proposed to generate the desired cycles in balanced hypercubes. In this paper, the authors develop systematic linear time algorithm to construct cycles and Hamiltonian cycles for the balanced hypercube.

A Linear Time Algorithm for Embedding Christmas Trees into Certain Trees

2015 ◽  
Vol 25 (04) ◽  
pp. 1550008
Author(s):  
Indra Rajasingh ◽  
R. Sundara Rajan ◽  
Paul Manuel
Keyword(s):  
Lower Bound ◽  
Interconnection Network ◽  
Linear Time ◽  
Graph Embedding ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Christmas Trees ◽  
Host Graph

Graph embedding is an important technique that maps a logical graph into a host graph, usually an interconnection network. In this paper, we compute the exact wirelength of embedding Christmas trees into trees. Moreover, we present an algorithm for embedding Christmas trees into caterpillars with dilation 3 proving that the lower bound obtained in [30] is sharp. Further, we solve the maximum subgraph problem for Christmas trees and provide a linear time algorithm to compute the exact wirelength of embedding Christmas trees into trees.

A PARALLEL ALGORITHM FOR ENCLOSED AND ENCLOSING TRIANGLES

1992 ◽  
Vol 02 (02) ◽  
pp. 191-214 ◽  
Author(s):  
SHARAT CHANDRAN ◽  
DAVID M. MOUNT
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Convex Polygon ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
New Techniques ◽  
Crcw Pram

We consider the problems of computing the largest area triangle enclosed within a given n-sided convex polygon and the smallest area triangle which encloses a given convex polygon. We show that these problems are closely related by presenting a single sequential linear time algorithm which essentially solves both problems simultaneously. We also present a cost-optimal parallel algorithm that solves both of these problems in O( log log n) time using n/ log log n processors on a CRCW PRAM. In order to achieve these bounds we develop new techniques for the design of parallel algorithms for computational problems involving the rotating calipers method.

scholarly journals Practical Wavelet Tree Construction

2021 ◽  
Vol 26 ◽  
pp. 1-67
Author(s):  
Patrick Dinklage ◽  
Jonas Ellert ◽  
Johannes Fischer ◽  
Florian Kurpicz ◽  
Marvin Löbel
Keyword(s):  
Parallel Algorithms ◽  
Shared Memory ◽  
Distributed Memory ◽  
Auxiliary Information ◽  
Parallel Computers ◽  
External Memory ◽  
Sequential Algorithms ◽  
Bottom Up ◽  
Memory Efficiency ◽  
Tree Construction

We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves. Most of our algorithms are also adapted to the wavelet matrix , a variant that is particularly suited for large alphabets.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

A Linear time algorithm for deciding security

1976 ◽  
Author(s):  
A. K. Jones ◽  
R. J. Lipton ◽  
L. Snyder
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm

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.

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