Abstract

this paper is to demonstrate the generality of two techniques used in [6] to develop an MDEPQ representation from an MPQ representation - height biased leftist trees. These methods - total correspondence and leaf correspondence - may be used to arrive at efficient DEPQ and MDEPQ data structures from PQ and MPQ data structures such as the pairing heap [8; 18], Binomial and Fibonacci heaps [9], and Brodal's FMPQ [2] which also provide efficient support for the operation: --Delete(Q,p): delete and return the element located at p We begin, in Section 2, by reviewing a rather straightforward way, dual priority queues, to obtain a (M)DEPQ structure from a (M)PQ structure. This method [2; 6] simply puts each element into both a minPQ and a maxPQ. In Section 3, we describe the total correspondence method and in Section 4, we describe leaf correspondence. Both sections provide examples of PQs and MPQs and the resulting DEPQs and MDEPQs. Section 5 gives complexity results. In Section 6, we provide the result of experiments that compare the performance of the MDEPQs based on height biased leftist tree [7], pairing heaps [8; 18], and FMPQs [2]. For reference purpose, we also provide run times for the splay tree data structure [16]. Although splay trees were not specifically designed to represent DEPQs, it is easy min Heap max Heap Fig. 1. Dual heap structure to use them for this purpose. Note that splay trees do not provide efficient support for the Meld operation

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