An Algorithm for Constructing Graceful Tree from an Arbitrary Tree

2013 ◽  
pp. 267-273
Author(s):  
G. Sethuraman ◽  
P. Ragukumar
Keyword(s):  
Arbitrary Tree

Towards Optimal Embedding of an Arbitrary Tree in a Graceful Tree

2015 ◽  
Vol 48 ◽  
pp. 73-80
Author(s):  
G. Sethuraman ◽  
P. Ragukumar
Keyword(s):  
Arbitrary Tree

OPTIMALITY AND SELF-STABILIZATION IN ROOTED TREE NETWORKS

1999 ◽  
Vol 09 (03) ◽  
pp. 313-323
Author(s):  
FRANCK PETIT ◽  
VINCENT VILLAIN
Keyword(s):  
Rooted Tree ◽  
The State ◽  
Extra Cost ◽  
Tree Networks ◽  
Token Circulation ◽  
Self Stabilization ◽  
Legitimate State ◽  
Arbitrary Tree

In this paper, we consider arbitrary tree networks where every processor, except one, called the root, executes the same program. We show that, to design a depth-first token circulation protocol in such networks, it is necessary to have at least [Formula: see text] configurations, where n is the number of processors in the network and Δi is the degree of processor pi. We then propose a depth-first token circulation algorithm which matches the above minimal number of configurations. We show that the proposed algorithm is self-stabilizing, i.e., the system eventually recovers itself to a legitimate state after any perturbation modifying the state of the processors. Hence, the proposed algorithm is optimal in terms of the number of configurations and no extra cost is involved in making it stabilizing.

scholarly journals THEORY OF DIGITAL FILTER BANKS REALIZED VIA MULTIVARIATE EMPIRICAL MODE DECOMPOSITION

2014 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
MIN-SUNG KOH ◽  
DANILO P. MANDIC ◽  
ANTHONY G. CONSTANTINIDES
Keyword(s):  
Empirical Mode Decomposition ◽  
Filter Banks ◽  
Tree Structure ◽  
Perfect Reconstruction ◽  
Tree Structures ◽  
Frequency Bands ◽  
Multivariate Empirical Mode Decomposition ◽  
Mode Decomposition ◽  
Digital Filter Banks ◽  
Arbitrary Tree

Undecimated and decimated multivariate empirical mode decomposition filter banks (MEMDFBs) are introduced in order to incorporate MEMD equipped with downsampling into any arbitrary tree structure and provide flexibility in the choice of frequency bands. Undecimated MEMDFBs show the same results as those of original MEMD for an octave tree structure. Since the exact cut-off frequencies of MEMD are not known (i.e. due to data-driven decomposition), employing just simple downsampling in MEMD might cause aliasing. However, decimated MEMDFBs in this paper achieve perfect reconstruction with aliasing cancelled for any arbitrary tree. Applications of decimated/undecimated MEMDFBs for speech/audio and image signals are also included. Since decimated MEMDFBs can be applied into any arbitrary tree structure, this extends into MEMD packets. Arbitrary tree structures in decimated MEMDFBs also lead to more diverse choices in frequency bands for various multivariate applications requiring decimations.

SUBTREE ISOMORPHISM IS IN DLOG FOR NESTED TREES

1996 ◽  
Vol 07 (02) ◽  
pp. 161-167 ◽  
Author(s):  
RAYMOND GREENLAW
Keyword(s):  
Interesting Class ◽  
Arbitrary Tree ◽  
Subtree Isomorphism

This research shows subtree isomorphism is in DLOG, and hence [Formula: see text], for nested trees. To our knowledge this result provides the first interesting class of trees for which the problem is in a non-randomized version of [Formula: see text]. We also show that one can determine whether or not an arbitrary tree is a nested tree in DLOG.

An algorithm to recognize weak roman domination stable trees under vertex deletion

2020 ◽  
Vol 12 (04) ◽  
pp. 2050049
Author(s):  
B. Mahavir ◽  
P. Roushini Leely Pushpam ◽  
M. Kamalam
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Roman Domination ◽  
Positive Weight ◽  
Roman Domination Number ◽  
Roman Dominating Function ◽  
Linear Time Algorithms ◽  
The Given ◽  
Arbitrary Tree

Let [Formula: see text] be a graph and [Formula: see text] be a function. A vertex [Formula: see text] with weight [Formula: see text] is said to be undefended with respect to [Formula: see text], if it is not adjacent to any vertex with positive weight. The function [Formula: see text] is a weak Roman dominating function (WRDF) if each vertex [Formula: see text] with [Formula: see text] is adjacent to a vertex [Formula: see text] with [Formula: see text] such that the function [Formula: see text] defined by [Formula: see text], [Formula: see text] and [Formula: see text] if [Formula: see text], has no undefended vertex. The weight of [Formula: see text] is [Formula: see text]. The weak Roman domination number, denoted by [Formula: see text], is the minimum weight of a WRDF on [Formula: see text]. In this paper, we present two linear time algorithms one that obtains the weak Roman domination number of an arbitrary tree and the labeling of its vertices, to produce the weak Roman domination number, and the other, that determines whether the given tree is in [Formula: see text].

scholarly journals EFFECTIVE SUPERPOTENTIALS FOR SO/Sp WITH FLAVOR FROM MATRIX MODELS

2003 ◽  
Vol 18 (16) ◽  
pp. 1113-1126 ◽  
Author(s):  
YUTAKA OOKOUCHI ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Gauge Theories ◽  
Tree Level ◽  
Arbitrary Tree

We study matrix models related to SO/Sp gauge theories with flavors. We give the effective superpotentials for gauge theories with arbitrary tree level superpotential up to first instanton level. For quartic tree level superpotential, we obtained exact one-cut solution. We also derive Seiberg–Witten curve for these gauge theories from matrix model argument.

scholarly journals Embedding of C_n^2 and C_(n-1)^2+K_1 in to Arbitrary Tree

2013 ◽  
Vol 61 (8) ◽  
pp. 27-30
Author(s):  
Vijender Kumar ◽  
Anil Kumar
Keyword(s):  
Arbitrary Tree

scholarly journals On $m$-Closed Graphs

10.37236/4406 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Leila Sharifan ◽  
Masoumeh Javanbakht
Keyword(s):  
Gröbner Basis ◽  
Lexicographic Order ◽  
Primary Decomposition ◽  
Equivalent Condition ◽  
Edge Ideal ◽  
Grobner Basis ◽  
Arbitrary Tree

A graph is closed when its vertices have a labeling by $[n]$ such that the binomial edge ideal $J_G$ has a quadratic Gröbner basis with respect to the lexicographic order induced by $x_1 > \ldots > x_n > y_1> \ldots > y_n$. In this paper, we generalize this notion and study the so called $m$-closed graphs. We find equivalent condition to $3$-closed property of an arbitrary tree $T$. Using it, we classify a class of $3$-closed trees. The primary decomposition of this class of graphs is also studied.

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