Cross-Lingual Mapping (CLM) establishes semantic relations between source and target concepts to align two resources lexicalized in different languages, e.g., ontologies, thesauri, or concept inventories, or to enrich a multilingual resource. In this paper, we focus on purely lexical matching algorithms to support CLM between lexically-rich resources, where concepts can be identified by synsets. The key idea of these algorithms is to use the results of word translations as evidence to map synsets lexicalized in different languages. We propose a new cross-lingual similarity measure inspired by a classification-based mapping semantics. Then we apply a novel local similarity optimization method to select the best matches for each source synset. To evaluate our approach we use wordnets in four different languages, which have been manually mapped to the English WordNet. Results show that despite our method uses only lexical information about the concepts, it obtains good performance and significantly outperforms several baseline methods.