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Symbol or phrase

Symbol or phrase	Latex format (italicize symbols)	Definition	Author	Comment	Editing comments
p	p	Number of processors or cores	Sushil Prasad	Processors, cores, and nodes are alternative ways of describing the number of processing units employed. The same symbol can be used if the description of a parallel algorithm or program uses “processes” or another abstraction for processing units
T1*	$T_{1}^{}$ $T_{1}^{}$	Fastest sequential time		This (usually) corresponds to the best sequential algorithm
Tp	T_p	Execution time of a parallel program/algorithm using p processors		T1 is thus the time taken by a parallel program using one processor and may involve parallel overheads. As compared with this, T1* is the pure sequential time
Sp	S_p	(Absolute) speedup of a parallel program using p processors compared with the fastest sequential time		Thus, the “absolute speedup” is defined as $S_{p} = T_{1}^{} / T_{p}$ $S_{p} = T_{1}^{} / T_{p}$ . T₁/T_p is the “relative speedup,” comparing a parallel program’s performance relative to its own performance using one processor
Cost		Cost of a parallel program		Cost = pT_p
Work		Total work collectively done by all processors		Work <= cost
Ep	E_p	Efficiency of a parallel program		$E_{p} = S_{p} / p = T_{1}^{} / p T_{p} = T_{1}^{} / cost$ $E_{p} = S_{p} / p = T_{1}^{} / p T_{p} = T_{1}^{} / cost$
Cost-optimal		A parallel algorithm whose cost is of the same order as $T_{1}^{}$ $T_{1}^{}$
G	G	Graph G		G = (V,E)
V	V	Set of nodes in graph G
E	E	Set of edges in graph G
n, m	n, m	Variables related to the size of the input	Anshul Gupta	Lower case letters such as n, m, etc., should be used to denote variables that determine the size of the input; for example, a set of n records, or an n × m matrix, or a graph with n vertices and m edges, etc.
Design pattern		A description of an effective solution to a recurring problem in a particular context	Dick Brown
N	N	Input size	Ramachandran Vaidyanathan	Uppercase is useful when N = 2^k is a power of 2
l	ℓ	Level of node in a tree	Ramachandran Vaidyanathan
t	t_i	Time-related quantity	Ramachandran Vaidyanathan
x’, X’	x^′ or X^′	Complement of a Boolean variable x or X	Ramachandran Vaidyanathan
< a,b >	< a,b >	Doublet or ordered pair < a,b >	Ramachandran Vaidyanathan
oplus	⊕	Generic associative operator	Thomas Cormen	When describing reduce and scan operations, we need a generic operator
@	@	Operator to perform segmented scans via unsegmented scans	Thomas Cormen	When performing segmented scan operations, we use a special operator to use the mechanism for unsegmented scans

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