We present an abstract framework for verifying concurrent algorithms on search data structures that support dictionaries. The framework can be specialized to every search data structure we know, from linked lists to complex B-trees. We obtain this framework by instantiating RGSep, which is a program logic that combines rely-guarantee reasoning and separation logic. RGSep is parameterized by a so-called resource algebra, which is typically the standard heap model of separation logic. Instead of using the standard heap model, we develop a new resource algebra that enables compositional reasoning about search graphs. Using this search graph model, we obtain simple correctness proofs of complex concurrent dictionary algorithms. The algorithms and proofs abstract from the specific search data structure that the algorithm operates on and can then be refined to a concrete data structure implementation.