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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)
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)
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)
skos:notation
  • RIV/00216208:11320/07:00004470!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 1;12
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 439333
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/07:00004470
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Complexity; Balanced; Vertex; Ordering; Problem (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • FR - Francouzská republika
http://linked.open...ontrolniKodProRIV
  • [ED00DE774C72]
http://linked.open...i/riv/nazevZdroje
  • Discrete Mathematics and Theoretical Computer Science
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 9
http://linked.open...iv/tvurceVysledku
  • Kratochvíl, Jan
  • Kára, Jan
http://linked.open...n/vavai/riv/zamer
issn
  • 1365-8050
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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