On-line version of Rabinovitch theorem for proper intervals

Bosek, Bartłomiej; Kloch, Kamil; Krawczyk, Tomasz; Micek, Piotr

doi:10.1016/j.disc.2012.02.008

Discrete Mathematics

2012

DOI: 10.1016/j.disc.2012.02.008

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On-line version of Rabinovitch theorem for proper intervals

Bartłomiej Bosek

Kamil Kloch

Tomasz Krawczyk

et al.

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Cited by 2 publications

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“…This of course provides more information to Algorithm and typically the value of the resulting game is different. Authors cover this new variant of the game in [16].…”

mentioning

confidence: 99%

On-Line Dimension of Semi-Orders

Bosek

Kloch

Krawczyk

et al. 2012

Order

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We analyze the on-line dimension of partially ordered sets as a value of a two-person game between Algorithm and Spoiler. The game is played in rounds. Spoiler presents an on-line order of width at most w, one point at a time. Algorithm maintains its realizer, i.e., the set of d linear extensions which intersect to the presented order. Algorithm may not change the ordering of the previously introduced elements in the existing linear extensions. The value of the game val(w) is the least d such that Algorithm has a strategy against Spoiler presenting any order of width at most w. For interval orders Hopkins showed that val(w) 4w − 4. We analyze the on-line dimension of semi-orders i.e., interval orders admitting a unit-length representation. For up-growing semi-orders of width w we prove a matching lower and upper bound of w. In the general (not necessarily up-growing) case we provide an upper bound of 2w.

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“…This of course provides more information to Algorithm and typically the value of the resulting game is different. Authors cover this new variant of the game in [16].…”

mentioning

confidence: 99%

On-Line Dimension of Semi-Orders

Bosek

Kloch

Krawczyk

et al. 2012

Order

Self Cite

View full text Add to dashboard Cite

show abstract

Dimension of Restricted Classes of Interval Orders

Keller

Trenk

Young

2022

Graphs and Combinatorics

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On-line version of Rabinovitch theorem for proper intervals

Cited by 2 publications

References 4 publications

On-Line Dimension of Semi-Orders

On-Line Dimension of Semi-Orders

Dimension of Restricted Classes of Interval Orders

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