Complex sentence: Most algorithms will test many possibilities for each partition until finding a good compromise and might also keep backtracking information in memory so that if a branch of the tree is found to be unsatisfactory other alternative partitions may be tried.
Split into simpler sentences: Most algorithms will test many possibilities for each partition until they find a good compromise. They might also keep backtracking information in memory, so that if a branch of the tree is found to be unsatisfactory, other alternative partitions may be tried.