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The IP address lookup has been a major challenge for Internet routers. This is accompanied with a background of advances in link bandwidth and rapid growth in Internet traffic and the number of networks. This survey paper explores binary search algorithms as a simple and efficient approach to the IP address lookup problem. Binary search algorithms are categorized as algorithms based on the trie structure, algorithms performing binary search on prefix values, and algorithms performing binary search on prefix lengths. In this paper, algorithms in each category are described in terms of their data structures, routing tables, and performance. Performance is evaluated with respect to pre-defined metrics, such as search speed and memory requirement. Table update, scalability toward large routing data, and the migration to IPv6 are also discussed. Simulation results are shown for real routing data with sizes of 15000 to 227000 prefixes acquired from backbone routers. Suggestions are made for the choice of algorithms depending on the table size, routing data statistics, or implementation flexibility.