Indexing Discrete Sets in a Label Setting Algorithm for Solving the Elementary Shortest Path Problem with Resource Constraints

Abstract

Stopping exploration of the search space regions that can be proven to contain only inferior solutions is an important acceleration technique in optimization algorithms. This study is focused on the utility of trie-based data structures for indexing discrete sets that allow to detect such a state faster. An empirical evaluation is performed in the context of index operations executed by a label setting algorithm for solving the Elementary Shortest Path Problem with Resource Constraints. Numerical simulations are run to compare a trie with a HAT-trie, a variant of a trie, which is considered as the fastest in-memory data structure for storing text in sorted order, further optimized for efficient use of cache in modern processors. Results indicate that a HAT-trie is better suited for indexing sparse multi dimensional data, such as sets with high cardinality, offering superior performance at a lower memory footprint. Therefore, HAT-tries remain practical when tries reach their scalability limits due to an expensive memory allocation pattern. Authors leave a final note on comparing and reporting credible time benchmarks for the Elementary Shortest Path Problem with Resource Constraints.