Pubblicazioni

Autori:

E., Köhler; C., Liebchen; G., Wünsch; Rizzi, Romeo

Titolo:

Lower bounds for strictly fundamental cycle bases in grid graphs.

Anno:

2009

Tipologia prodotto:

Articolo in Rivista

Tipologia ANVUR:

Articolo su rivista

Lingua:

Inglese

Formato:

A Stampa

Referee:

Sì

Nome rivista:

NETWORKS

ISSN Rivista:

0028-3045

N° Volume:

53

Numero o Fascicolo:

2

Intervallo pagine:

191-205

Parole chiave:

combinatorial optimization; minimum cycle basis; planar dual; spanning tree; asymptotic analysis

Breve descrizione dei contenuti:

Consider the following problem: compute a spanning tree such that the sum of the lengths of its induced fundamental circuits is as small as possible. We motivate why planar square grid graphs are very relevant instances for this problem. In particular, other contributions already showed that the identification of strong lower bounds is highly challenging. Asymptotically, for a graph on n vertices, Alon et al. [SIAM J Comput 24(1995), 78–100] obtained a lower bound of Ω(n log n). We raise the n log n coefficient by a factor of 325. Concerning optimality proofs, the largest grid for which provably optimum solutions were known is 6 × 6, and it was obtained by massive MIP computing power. Here, we present a combinatorial optimality proof even for the 8 × 8 grid. These two results are complemented by new combinatorial lower bounds for the dimensions in which earlier empirical computations were performed, i.e., for up to 10,000 vertices.

Id prodotto:

71474

Handle IRIS:

11562/409559

depositato il:

15 luglio 2012

ultima modifica:

17 novembre 2022

Citazione bibliografica:

E., Köhler; C., Liebchen; G., Wünsch; Rizzi, Romeo, Lower bounds for strictly fundamental cycle bases in grid graphs. «NETWORKS» , vol. 53 , n. 2 , 2009 , pp. 191-205

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