TY - JOUR

T1 - Estimation of Expressions’ Complexities for Two-Terminal Directed Acyclic Graphs

AU - Korenblit, Mark

AU - Levit, Vadim E.

N1 - Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2017/12

Y1 - 2017/12

N2 - The paper investigates relationship between algebraic expressions and graphs. Our intention is to simplify graph expressions and eventually find their shortest representations. We prove the decomposition lemma which asserts that the shortest expression of a subgraph of a graph G is not larger than the shortest expression of G. Using this finding, we estimate an upper bound of a size of the shortest expression for any two-terminal directed acyclic graph.

AB - The paper investigates relationship between algebraic expressions and graphs. Our intention is to simplify graph expressions and eventually find their shortest representations. We prove the decomposition lemma which asserts that the shortest expression of a subgraph of a graph G is not larger than the shortest expression of G. Using this finding, we estimate an upper bound of a size of the shortest expression for any two-terminal directed acyclic graph.

KW - Two-terminal directed acyclic graph

KW - algebraic expression

KW - complexity

KW - edge-labeled graph

KW - series-parallel graph

UR - http://www.scopus.com/inward/record.url?scp=85036548520&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2017.11.005

DO - 10.1016/j.endm.2017.11.005

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AN - SCOPUS:85036548520

SN - 1571-0653

VL - 63

SP - 109

EP - 116

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -