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This paper addresses the problem of systematic exploration of an unfamiliar environment to build a qualitative map by searching for recognizable targets. While exploring, a map is constructed which contains a set of regions of free space delineated by recognizable targets (landmarks) and the connectivity (adjacency and overlap) of these regions. As the robot moves along a trajectory while tracking a landmark, a region of free space is swept out. By representing a collection of free regions and their region-to-region connectivity as a graph, path planning amounts to graph search, and execution of the plan by a robot amounts to local movements to enter into the next free region. Both for exploration and for navigation, no metric information about the robot's path nor absolute coordinates of its position or of landmark locations are required or recorded. After exploring, the robot produces a compact map which covers a large area, and provides information for fast self-localization and flexible path planning.