35 research outputs found
Fast strategies in biased Maker--Breaker games
We study the biased Maker--Breaker positional games, played on the
edge set of the complete graph on vertices, . Given Breaker's bias
, possibly depending on , we determine the bounds for the minimal number
of moves, depending on , in which Maker can win in each of the two standard
graph games, the Perfect Matching game and the Hamilton Cycle game
Fast winning strategies in Avoider-Enforcer games
In numerous positional games the identity of the winner is easily determined.
In this case one of the more interesting questions is not {\em who} wins but
rather {\em how fast} can one win. These type of problems were studied earlier
for Maker-Breaker games; here we initiate their study for unbiased
Avoider-Enforcer games played on the edge set of the complete graph on
vertices. For several games that are known to be an Enforcer's win, we
estimate quite precisely the minimum number of moves Enforcer has to play in
order to win. We consider the non-planarity game, the connectivity game and the
non-bipartite game
Linear Time Algorithm for Optimal Feed-link Placement
Given a polygon representing a transportation network together with a point p
in its interior, we aim to extend the network by inserting a line segment,
called a feed-link, which connects p to the boundary of the polygon. Once a
feed link is fixed, the geometric dilation of some point q on the boundary is
the ratio between the length of the shortest path from p to q through the
extended network, and their Euclidean distance. The utility of a feed-link is
inversely proportional to the maximal dilation over all boundary points.
We give a linear time algorithm for computing the feed-link with the minimum
overall dilation, thus improving upon the previously known algorithm of
complexity that is roughly O(n log n)