Section: New Results

Tree representations

We found an intriguing duality between two well-known representations of trees [12]. This work concerns data structures and succinct tree representations. The Balanced Parenthesis representation of trees consists of encoding the structure of any tree using a series of opening and closing parentheses. The DFUDS representation is similar, but differs in how each node is encoded (also using parentheses). By relating both BP and DFUDS representations, we obtained improvements for a basic fundamental problem: the Minimum Length Interval Query problem. We also reported unnoted commonalities in recent solution to the Range Minimum Query problem.