Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to a set of constraints. While solving a CSP is an NP-complete task in general, it is believed that efficiency can be significantly improved by exploiting the characteristics of the problem. In this paper, we present a solution synthesis algorithm called $omega$-CDGT which is an existing algorithm named CDGT augmented with a constraint representative graph called $omega$-graph. We show that the worst-case complexity of the $omega$-CDGT algorithm is better than other related algorithms.