WALKING IN AN ARRANGEMENT TOPOLOGICALLY

Abstract

We present topological walk, an on-line algorithm for computing a walk in an arrangement. Here, a walk is a visit to the cells of an arrangement in an order such that consecutive cells are adjacent to each other. The algorithm can walk in a part of an arrangement efficiently; more precisely, given an arrangement of n lines in a convex region containing K cells, a walk is performed in O(K + n log n) time and O(n) working space. Several optimal-cell-finding problems can be solved efficiently applying the topological walk. Further, a construction of a spanning tree with maximum node degree three of the dual graph of an arrangement is given.