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Radio frequency identification (RFID) is a proven automation technology finding application in various commercial sectors. These applications involve locating all tagged items automatically using available RFID readers. RFID readers are of two types, fixed and mobile. The number of readers required to cover an area depends on factors such as the properties of the reader, tag and the shape of the area to be covered. This paper presents an algorithm to find the minimum number of fixed RFID readers required for complete coverage of an area of irregular shape. This approach, which applies the Graham's scan algorithm of computational geometry, can be used for buildings, warehouses, etc., of any shape. The algorithm determines the required number of readers by considering the interrogation range of the reader. A methodology of forming the convex hull/polygon covering the irregular area, and subsequently placing the readers at specified locations within the polygon based on the properties of the reader is discussed here. A sample tiling of an irregularly shaped floor space is shown as an example, and applications of the tiling algorithm are indicated by giving verbal sketches of automation systems for a food court, a parking lot, and an airport baggage tracking system that can make use of it.