Forum for Direct Confrontation

iterated Swartz Set [#2330]

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MatthieuWalraet: iterated Swartz Set (2010-07-22 00:04) [#7826]

Matthieu Walraet: I move this from main page. The example may be confusing as it is not how actual algo works.

willemien: I don't understand the iterations. It looks like an iterated Swartz Set [ext] http://en.wikipedia.org/wiki/Schwartz_set if that is the case it should be

  • 1st iteration
 #                       Rank   Club Pt                                           MMS  DC SOS-1 Rating
 7  Burzo Cornel          6D RO BaMa 3 18+/b0  4-/w0 12+/b0  3-/w0  9+/b0  1-/b0  37   3   190  562
 8  Simara Jan            6D CZ KaVa 3  3-/w0 23+/b0 15-/w0 10+/b0 16+/w0  4-/b0  37   2   185  523
 9  Zhurakovskyj Bohdan   5D UA Rivn 3 15-/b0 22+/w0 10+/w0  4-/b0  7-/w0 18+/b0  37   2   184  432
10  Florescu Ion          6D RO Pits 3  1-/b0 13+/w0  9-/b0  8-/w0 19+/b0 17+/w0  37   1   187  561
11  Jabarin Ali           5D IL TAv  3  4-/w0 16+/b0  6-/b0 18+/w0 13+/b0  5-/w0  37   1   187  457
12  Lin Viktor            5D AT Gote 3  5-/w0 14+/b0  7-/w0 19+/w0 15+/b0  6-/b0  37   1   186  446
13  Corlan Lucian         5D RO Bucu 3  6-/w0 10-/b0 24+/w0 25+/b0 11-/w0 15+/b0  37   0   183  428
14  Serban Mihai_Valentin 4D RO Bist 4 19+/w0 12-/w0 30+/b0  5-/b0 22+/b0 16+/w0  37   0   182  349

Burzo, Simara, Zhurakovskyj, Florescu, Jabarin and Lin all defeated at least one player in the group so should not be last. Corlan and Serban have not. Corlan and Serban are therefore both removed.

  • 2nd iteration
 #                       Rank   Club Pt                                           MMS  DC SOS-1 Rating
 7  Burzo Cornel          6D RO BaMa 3 18+/b0  4-/w0 12+/b0  3-/w0  9+/b0  1-/b0  37   3   190  562
 8  Simara Jan            6D CZ KaVa 3  3-/w0 23+/b0 15-/w0 10+/b0 16+/w0  4-/b0  37   2   185  523
 9  Zhurakovskyj Bohdan   5D UA Rivn 3 15-/b0 22+/w0 10+/w0  4-/b0  7-/w0 18+/b0  37   2   184  432
10  Florescu Ion          6D RO Pits 3  1-/b0 13+/w0  9-/b0  8-/w0 19+/b0 17+/w0  37   1   187  561
11  Jabarin Ali           5D IL TAv  3  4-/w0 16+/b0  6-/b0 18+/w0 13+/b0  5-/w0  37   1   187  457
12  Lin Viktor            5D AT Gote 3  5-/w0 14+/b0  7-/w0 19+/w0 15+/b0  6-/b0  37   1   186  446

Burzo, Simara, Zhurakovskyj defeated at least one player in the group so should not be last. Florescu, Jabarin and Lin have not. Florescu, Jabarin and Lin are therefore all removed.

  • 3rd iteration
 #                       Rank   Club Pt                                           MMS  DC SOS-1 Rating
 7  Burzo Cornel          6D RO BaMa 3 18+/b0  4-/w0 12+/b0  3-/w0  9+/b0  1-/b0  37   3   190  562
 8  Simara Jan            6D CZ KaVa 3  3-/w0 23+/b0 15-/w0 10+/b0 16+/w0  4-/b0  37   2   185  523
 9  Zhurakovskyj Bohdan   5D UA Rivn 3 15-/b0 22+/w0 10+/w0  4-/b0  7-/w0 18+/b0  37   2   184  432

Only Burzo defeated a player in the group and is therefore the winner.

Note that this procedure does not always give a winner if A defeated B, B defeated C and C defeated B this tiebreaker ties the 3 players.

isd: No, for a 'cycle of players' (group of tied players) the one(s) with the lowest secondary tiebreaker are removed. Direct Confrontation needs a secondary tiebreaker to operate. See the 3rd and 4th points in the definition provided by Open Gotha

MatthieuWalraet: The math name for Direct Confrontation is Topological sorting [ext] http://en.wikipedia.org/wiki/Topological_sorting

X
132.246.27.86: Re: iterated Swartz Set (2010-07-22 21:28) [#7828]

Is this a Schwartz set? The definition requires that players have beaten all opponents outside the set, which is not necessarily the case.

MatthieuWalraet: Re: iterated Swartz Set (2010-07-23 15:39) [#7829]

If I correctly understand Schartz Set, in this case it should be 7, 8 and 11.

Anyway, the direct confrontation example done by isd and HermanHiddema on main page is correct. That's why I moved Willemien question here.

willemien: Re: iterated Swartz Set (2010-07-27 08:36) [#7843]

To me it just all looked like the swartz set but then only applied to the players inside the tied group that is concidered ( so not concidering the players outside the group)

If you apply it to all players probably all the players that you are trying to break the tie between will be removed.

To MatthieuWalraet can you explain how you get to 7 8 and 11?. (maybe i am wrong)

193.111.93.130: Re: iterated Swartz Set (2010-08-03 13:47) [#7865]

Using definition in Wikipedia page, there is three Schwartz set components: {7} {8} and {11}, the Schwartz set is union of those, so {7, 8, 11}

 
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