We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a l...

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a l...

This paper proposes a new location problem of competitive facilities, e.g. shops. In the most studies of competitive facility location, the distance between the facilities and their customers is represented as the Euclid distance. The proposing location problem introduces the A-distance, proposed by Widmayer etc., for representing the situation that the directions which customers can move are g...

In this paper we propose the Online Connected Facility Location problem (OCFL), which is an online version of the Connected Facility Location problem (CFL). The CFL is a combination of the Uncapacitated Facility Location problem (FL) and the Steiner Tree problem (ST). We give a randomized O(log n)-competitive algorithm for the OCFL via the sample-and-augment framework of Gupta, Kumar, Pál, and ...