scholarly journals Positional Games and QBF: The Corrective Encoding

Author(s):  
Valentin Mayer-Eichberger ◽  
Abdallah Saffidine
Keyword(s):  
2000 ◽  
Vol 230 (1-2) ◽  
pp. 207-219 ◽  
Author(s):  
J.Mark Ettinger
Keyword(s):  

10.37236/559 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
József Balogh ◽  
Wojciech Samotij

Given a graph $G$ and positive integers $n$ and $q$, let ${\bf G}(G;n,q)$ be the game played on the edges of the complete graph $K_n$ in which the two players, Maker and Breaker, alternately claim $1$ and $q$ edges, respectively. Maker's goal is to occupy all edges in some copy of $G$; Breaker tries to prevent it. In their seminal paper on positional games, Chvátal and Erdős proved that in the game ${\bf G}(K_3;n,q)$, Maker has a winning strategy if $q < \sqrt{2n+2}-5/2$, and if $q \geq 2\sqrt{n}$, then Breaker has a winning strategy. In this note, we improve the latter of these bounds by describing a randomized strategy that allows Breaker to win the game ${\bf G}(K_3;n,q)$ whenever $q \geq (2-1/24)\sqrt{n}$. Moreover, we provide additional evidence supporting the belief that this bound can be further improved to $(\sqrt{2}+o(1))\sqrt{n}$.


1997 ◽  
Vol 174 (1-2) ◽  
pp. 247-249
Author(s):  
Yõhei Yamasaki
Keyword(s):  

1998 ◽  
Vol 7 (4) ◽  
pp. 339-351 ◽  
Author(s):  
MAŁGORZATA BEDNARSKA

Let TBin(N, n, q) be the game on the complete graph KN in which two players, the Breaker and the Maker, alternately claim one and q edges, respectively. The Maker's aim is to build a binary tree on n<N vertices in n−1 turns while the Breaker tries to prevent him from doing so. It is shown that, for every constant ε>0, there exists n0 such that, for every n[ges ]n0, the Breaker has a winning strategy in TBin(N, n, q) if q>(1+ε)N/logn, while, for q<(1−ε)N/logn, the game TBin(N, n, q) can be won by the Maker provided that n=o(N).


2005 ◽  
Vol 14 (5-6) ◽  
pp. 649 ◽  
Author(s):  
JÓZSEF BECK
Keyword(s):  

2018 ◽  
Vol 6 (5) ◽  
pp. 65
Author(s):  
Melih Balyan ◽  
Faik Vural

Futsal, which can be defined as a new sports branch compared to football, has some shortcomings in comparison with football as well according to the studies carried out.  Studies have rather focused on the movement characteristics of futsal players during the game and the physiological effects of games. On the other hand, there are only a limited number of studies conducted on game analysis. Therefore, as the primary goal of the present study, offensive variations that ended up as goals in all matches played in Futsal World Cup were analyzed. As the secondary goal, these parameters were studied in terms of the teams’ winning-drawing-losing states during games. In the present study, a total of 52 matches of the teams playing in 2016 FIFA Futsal World Championship were analyzed. The analyses of the games were performed using the hand notation method. Differences between offensive variations (Diagonal, parallel, central and transition game forms, set games etc.) and the goals scored (shots taken, shots at goal, the area where the goals were scored, the way the goals were scored, the area where the foot hit the ball, block shoots etc.) were determined with One-way Anova and Kruskal-Wallis tests on SPSS version 20 in terms of 3 variables (win-loss-draw). The findings show that the winning teams had significantly more shots than the losing teams (10.80, 95%CI (from 3, 73 to 17, 87) and that the number of shots at goal was also higher (5.82, 95%CI (from 2, 43 to 9, 91) in terms of the teams’ winning-losing-drawing states. However, no statistically significant difference was found between the areas where the shots were taken and the points they ended up at the goal. As for position specific games, on the other hand, statistically significant differences were found in terms of winning, losing and drawing states during the game (central= χ2(2) = 10.500, p = .005, diagonal= χ2(2) = 17.142, p = .000, parallel= χ2(2) = 10.931, p = .004, transition= χ2(2) = 28,587 p = .000). No statistically significant difference was found between set games ending up with goals and the teams’ game score variables. The results obtained concerning offensive variations in a superior futsal championship reveal that positional games of dynamic style could be much more effective compared to set games of static starting positions in winning the game. Moreover, producing shooting positions and their accuracy levels seem to be an important factor affecting success. According to these results, it can be recommended that the trainings to be held should be designed to improve positional games that these should be planned as practices that result in shots.


2019 ◽  
Vol 78 (1) ◽  
pp. 1-30
Author(s):  
József Beck
Keyword(s):  

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