TY - JOUR

T1 - On lengths of edge-labeled graph expressions

AU - Korenblit, Mark

AU - Levit, Vadim E.

N1 - Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/10/15

Y1 - 2022/10/15

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

UR - http://www.scopus.com/inward/record.url?scp=85130775619&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2022.04.015

DO - 10.1016/j.dam.2022.04.015

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AN - SCOPUS:85130775619

SN - 0166-218X

VL - 319

SP - 583

EP - 594

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -