Review of Communication Complexity and Applications by Anup Rao and Amir Yehudayoff

2021 ◽  
Vol 52 (3) ◽  
pp. 11-13
Author(s):  
Michael Cadilhac
Keyword(s):  
Probability Theory ◽  
Data Structures ◽  
Communication Complexity ◽  
Circuit Complexity ◽  
Theoretical Computer Science ◽  
Vantage Point ◽  
Upper And Lower Bounds ◽  
Theoretical Computer ◽  
Communication Problems ◽  
Eye Opening

At its core, communication complexity is the study of the amount of information two parties need to exchange in order to compute a function. For instance, Alice receives a string of characters, Bob receives another, and they should decide whether these strings are the same with as few rounds of communication as possible. Multiple settings are conceivable, for instance with multiple parties or with randomness. Upper and lower bounds for communication problems rely on a wealth of mathematical tools, from probability theory to Ramsey theory, making this a complete and exciting topic. Further, communication complexity finds applications in different aspects of theoretical computer science, including circuit complexity and data structures. This usually requires to take a "communication" view of a problem, which in itself can be an eye-opening vantage point.

Guest Column

2021 ◽  
Vol 52 (2) ◽  
pp. 46-70
Author(s):  
A. Knop ◽  
S. Lovett ◽  
S. McGuire ◽  
W. Yuan
Keyword(s):  
Machine Learning ◽  
Approximation Algorithms ◽  
Computer Science ◽  
Data Structures ◽  
Coding Theory ◽  
Communication Complexity ◽  
Property Testing ◽  
Theoretical Computer Science ◽  
Streaming Algorithms ◽  
Theoretical Computer

Communication complexity studies the amount of communication necessary to compute a function whose value depends on information distributed among several entities. Yao [Yao79] initiated the study of communication complexity more than 40 years ago, and it has since become a central eld in theoretical computer science with many applications in diverse areas such as data structures, streaming algorithms, property testing, approximation algorithms, coding theory, and machine learning. The textbooks [KN06,RY20] provide excellent overviews of the theory and its applications.

scholarly journals SOME IMPORTANT APPLICATIONS OF SEMIGROUPS

2021 ◽  
Vol 2 (2) ◽  
pp. 317-321
Author(s):  
Iqra Liaqat ◽  
Wajeeha Younas
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Probability Theory ◽  
Markov Process ◽  
Computer Science ◽  
Finite Automata ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Regular Semigroups ◽  
Finite Semigroups

This Paper deals with the some important applications of semigroups in general and regular semigroups in particular.The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov process. In section 2 we have seen different areas of applications of semigroups. We identified some Applications in biology, Partial Differential equation, Formal Languages etc whose semigroup structures are nothing but regular.

scholarly journals Quadruple Roman Domination in Trees

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1318
Author(s):  
Zheng Kou ◽  
Saeed Kosari ◽  
Guoliang Hao ◽  
Jafar Amjadi ◽  
Nesa Khalili
Keyword(s):  
Open Neighborhood ◽  
Minimum Weight ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Upper And Lower Bounds ◽  
Discrete Mathematics ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Vertex Set ◽  
Roman Dominating Function

This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.

scholarly journals From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1036
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodríguez-Velázquez
Keyword(s):  
Vertex Cover ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Special Issue ◽  
Total Domination Number ◽  
Theoretical Computer ◽  
Graph Parameters ◽  
Semitotal Domination ◽  
Domination In Graphs

This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x∈V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X⊆V(G) is defined to be N(X)=⋃x∈XN(x), while the external neighbourhood of X is defined to be Ne(X)=N(X)∖X. Now, for every set X⊆V(G) and every vertex x∈X, the external private neighbourhood of x with respect to X is defined as the set Pe(x,X)={y∈V(G)∖X:N(y)∩X={x}}. Let Xw={x∈X:Pe(x,X)≠⌀}. The strong differential of X is defined to be ∂s(X)=|Ne(X)|−|Xw|, while the quasi-total strong differential of G is defined to be ∂s*(G)=max{∂s(X):X⊆V(G)andXw⊆N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

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