The 802.11 IEEE Standard has enabled low cost and effective wireless LAN services (WLAN). With the sales and deployment of WLAN based networks exploding, many people believe that they will become the fourth generation cellular system (4G) or a major portion of it. However, the small cell size of WLAN networks creates frequent hand-offs for mobile users. If the latency of these hand-offs is high, as previous studies have shown, then the users of synchronous multimedia applications such as voice over IP (VoIP) will experience excessive jitter. The dominating factor in WLAN hand-offs has been shown to be the discovery of the candidate set of next access points. In this paper, we describe the use of a novel and efficient discovery method using neighbor graphs and overlap graphs. Our method reduces the total number probed channels as well as the total time spent waiting on each channel. Our implementation results show that this approach reduces the overall probe time significantly when compared to other approaches. Furthermore, simulation results show that the effectiveness of our method improves as the number of non-overlapping channels increases, such as in the 5 GHz band used by the IEEE 802.11a standard. (UMIACS-TR-2003-118)