论文信息 - Improved Exploration of Rectilinear Polygons

Improved Exploration of Rectilinear Polygons

Exploring a polygon is the problem of a robot that does not have a map of its surroundings to see the complete polygon. In other words, for the robot to construct a map of the polygon. Exploration can be viewed as an online problem. Typical for online problems is that the solution method must make decisions based on past events but without knowledge about the future. In our case the robot does not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive factor of such a method is the ratio between the method's performance and the performance of the best method having full knowledge about the future. We prove a 5/3-competitive strategy for exploring a simple rectilinear polygon in the L1 metric. This improves the previous factor two bound of Deng, Kameda and Papadimitriou.

Bengt J. Nilsson | Sven Schuierer | Mikael Hammar | S. Schuierer | M. Hammar

[1] Rolf Klein,et al. The Polygon Exploration Problem , 2001, SIAM J. Comput..

[2] Mona Singh,et al. Piecemeal Learning of an Unknown Environment , 1993, COLT.

[3] Mihalis Yannakakis,et al. Shortest Paths Without a Map , 1989, Theor. Comput. Sci..

[4] Simeon C. Ntafos,et al. Optimum Watchman Routes , 1988, Inf. Process. Lett..

[5] Rolf Klein,et al. Searching for the kernel of a polygon—a competitive strategy , 1995, SCG '95.

[6] Jon M. Kleinberg,et al. On-line search in a simple polygon , 1994, SODA '94.

[7] Tak Wah Lam,et al. An on-line algorithm for navigating in unknown environment , 1993, Int. J. Comput. Geom. Appl..

[8] Alejandro López-Ortiz,et al. Going Home Through an Unknown Street , 1995, WADS.

[9] Wei-Pand Chin,et al. Shortest watchman routes in simple polygons , 1990, Discret. Comput. Geom..

[10] Amitava Datta,et al. Competitive searching in a generalized street , 1999, Comput. Geom..

[11] Robert E. Tarjan,et al. Amortized efficiency of list update and paging rules , 1985, CACM.

[12] Yoshihide Igarashi,et al. An Efficient Strategy for Robot Navigation in Unknown Environment , 1994, Inf. Process. Lett..

[13] Rolf Klein. Walking an Unknown Street with Bounded Detour , 1991, Comput. Geom..

[14] Amitava Datta,et al. Competitive Searching in Polygons - Beyond Generalised Streets , 1995, ISAAC.

[15] Xiaotie Deng,et al. How to learn an unknown environment. I: the rectilinear case , 1998, JACM.