Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A new framework for elimination-based data flow analysis using DJ graphs
ACM Transactions on Programming Languages and Systems (TOPLAS)
A new, simpler linear-time dominators algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Purely functional, real-time deques with catenation
Journal of the ACM (JACM)
Splay trees, Davenport-Schinzel sequences, and the deque conjecture
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Applications of forbidden 0-1 matrices to search tree and path compression-based data structures
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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A deque with heap order is a linear list of elements with real-valued keys that allows insertions and deletions of elements at both ends of the list. It also allows the findmin (alternatively findmax) operation, which returns the element of least (greatest) key, but it does not allow a general deletemin (deletemax) operation. Such a data structure is also called a mindeque (maxdeque). Whereas implementing heap-ordered deques in constant time per operation is a solved problem, catenating heap-ordered deques in sublogarithmic time has until now remained open. This paper provides an efficient implementation of catenable heap-ordered deques, yielding constant amortized time per operation. The important algorithmic technique employed is an idea that we call data-structural bootstrapping: we abstract heap-ordered deques by representing them by their minimum elements, thereby reducing catenation to simple insertion. The efficiency of the resulting data structure depends upon the complexity of a special case of path compression that we prove takes linear time.