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Description
| - Uvažujeme problém nalezení vyrovnaného uspořádání vrcholů grafu. Přesněji chceme minimalizovat součet přes všechny vrcholy $v$ z rozdílu počtu levých a pravých sousedů $v$. Jeden z našich hlavních výsledků je důkaz NP-úplnosti pro rovinné grafy s maximálním stupněm 4 a pro 5-regulární grafy. Na druhé straně ukážeme algoritmus běžící v polynomiálním čase, který určí, zda existuje uspořádání vrcholů s nevyvážeností menší než daná konstanta nebo zda daný multigraf se sudými stupni má 'téměř vyvážené' uspořádání. (cs)
- We consider the problem of finding a balanced ordering of the vertices of a graph. More precisely, we want to minimise the sum, taken over all vertices $v$, of the difference between the number of neighbours to the left and right of $v$. One of our main results is to prove NP-hardness for graphs with maximum degree four. Furthermore, we prove that the problem remains NP-hard for planar graphs with maximum degree four and for 5-regular graphs. On the other hand, we introduce a polynomial time algorithm that determines whether there is a vertex ordering with total imbalance smaller than a fixed constant, and a polynomial time algorithm that determines whether a given multigraph with even degrees has an `almost balanced' ordering.
- We consider the problem of finding a balanced ordering of the vertices of a graph. More precisely, we want to minimise the sum, taken over all vertices $v$, of the difference between the number of neighbours to the left and right of $v$. One of our main results is to prove NP-hardness for graphs with maximum degree four. Furthermore, we prove that the problem remains NP-hard for planar graphs with maximum degree four and for 5-regular graphs. On the other hand, we introduce a polynomial time algorithm that determines whether there is a vertex ordering with total imbalance smaller than a fixed constant, and a polynomial time algorithm that determines whether a given multigraph with even degrees has an `almost balanced' ordering. (en)
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Title
| - On the Complexity of the Balanced Vertex Ordering Problem
- On the Complexity of the Balanced Vertex Ordering Problem (en)
- O složitosti problému vyrovnaného uspořádání vrcholů (cs)
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skos:prefLabel
| - On the Complexity of the Balanced Vertex Ordering Problem
- On the Complexity of the Balanced Vertex Ordering Problem (en)
- O složitosti problému vyrovnaného uspořádání vrcholů (cs)
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skos:notation
| - RIV/00216208:11320/07:00004470!RIV08-MSM-11320___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(1M0545), Z(MSM0021620838)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/07:00004470
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Complexity; Balanced; Vertex; Ordering; Problem (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - FR - Francouzská republika
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Discrete Mathematics and Theoretical Computer Science
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Kratochvíl, Jan
- Kára, Jan
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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