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Functionally related genes co-evolve, probably due to selection pressures during evolution, This phenomenon leads to conservation of gene clusters across genomes, especially in microbial genomes. In this paper, we propose novel iterative constraint relaxation algorithms which make use of genome contexts to effectively remove noise and extract gene clusters: PairEGGS that generates gene clusters in a pair of genomes and MultiEGGS that combines gene clusters from genome pairs. Experiments showed that PairEGGS produced significantly larger gene clusters than existing algorithms, say FISH, and MultiEGGS was able to find gene clusters as large as of 118 genes that are common to three genomes. Both PairEGGS and MultiEGGS run fast enough to provide service on the web.