On lengths of edge-labeled graph expressions

Mark Korenblit; Vadim E. Levit

doi:10.1016/j.dam.2022.04.015

On lengths of edge-labeled graph expressions

Mark Korenblit, Vadim E. Levit

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

Abstract

This paper investigates relationship between algebraic expressions and graphs. Our intent is to simplify graph expressions and eventually find their shortest representations. We prove the monotonicity results allowing to assert that the length of a shortest expression of any subgraph of a given graph is not greater than the length of a shortest expression of the graph. We describe the decomposition method for generating expressions of complete st-dags (two-terminal directed acyclic graphs) and estimate the corresponding expression complexities. Using these findings, we present an 2^Olog²n upper bound for the length of a shortest expression for every n-vertex st-dag.

Original language	English
Pages (from-to)	583-594
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	319
DOIs	https://doi.org/10.1016/j.dam.2022.04.015
State	Published - 15 Oct 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Algebraic expression
Complexity
Decomposition
Edge-labeled graph
Series–parallel graph
Two-terminal directed acyclic graph

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10.1016/j.dam.2022.04.015

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AU - Levit, Vadim E.

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N2 - This paper investigates relationship between algebraic expressions and graphs. Our intent is to simplify graph expressions and eventually find their shortest representations. We prove the monotonicity results allowing to assert that the length of a shortest expression of any subgraph of a given graph is not greater than the length of a shortest expression of the graph. We describe the decomposition method for generating expressions of complete st-dags (two-terminal directed acyclic graphs) and estimate the corresponding expression complexities. Using these findings, we present an 2Olog2n upper bound for the length of a shortest expression for every n-vertex st-dag.

AB - This paper investigates relationship between algebraic expressions and graphs. Our intent is to simplify graph expressions and eventually find their shortest representations. We prove the monotonicity results allowing to assert that the length of a shortest expression of any subgraph of a given graph is not greater than the length of a shortest expression of the graph. We describe the decomposition method for generating expressions of complete st-dags (two-terminal directed acyclic graphs) and estimate the corresponding expression complexities. Using these findings, we present an 2Olog2n upper bound for the length of a shortest expression for every n-vertex st-dag.

KW - Algebraic expression

KW - Complexity

KW - Decomposition

KW - Edge-labeled graph

KW - Series–parallel graph

KW - Two-terminal directed acyclic graph

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

On lengths of edge-labeled graph expressions

Abstract

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Keywords

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