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

Mark Korenblit; Vadim E. Levit

doi:10.1016/j.endm.2017.11.005

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

Mark Korenblit
, Vadim E. Levit

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	109-116
Number of pages	8
Journal	Electronic Notes in Discrete Mathematics
Volume	63
DOIs	https://doi.org/10.1016/j.endm.2017.11.005
State	Published - Dec 2017

Keywords

Two-terminal directed acyclic graph
algebraic expression
complexity
edge-labeled graph
series-parallel graph

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10.1016/j.endm.2017.11.005

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abstract = "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.",

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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

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

Abstract

Keywords

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