Priority Queues with Multiple Time Fingers

A priority queue is presented that supports the operations insert and find-min in worst-case constant time, and delete and delete-min on element x in worst-case O(lg(min{w_x, q_x}+2)) time, where w_x (respectively q_x) is the number of elements inserted after x (respectively before x) and are still present at the time of the deletion of x. Our priority queue then has both the working-set and the queueish properties, and more strongly it satisfies these properties in the worst-case sense. We also define a new distribution-sensitive property---the time-finger property, which encapsulates and generalizes both the working-set and queueish properties, and present a priority queue that satisfies this property. In addition, we prove a strong implication that the working-set property is equivalent to the unified bound (which is the minimum per operation among the static finger, static optimality, and the working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [JACM 1985]. Accordingly, our priority queue satisfies other distribution-sensitive properties as the static finger, static optimality, and the unified bound.Comment: 14 pages, 4 figure

Smooth heaps and a dual view of self-adjusting data structures

We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within a natural model, to a corresponding BST algorithm with the same cost on a dual sequence of operations (i.e. the same sequence with the roles of time and key-space switched). This is the first general transformation between the two families of data structures. There is a rich theory of dynamic optimality for BSTs (i.e. the theory of competitiveness between BST algorithms). The lack of an analogous theory for heaps has been noted in the literature. Through our connection, we transfer all instance-specific lower bounds known for BSTs to a general model of heaps, initiating a theory of dynamic optimality for heaps. On the algorithmic side, we obtain a new, simple and efficient heap algorithm, which we call the smooth heap. We show the smooth heap to be the heap-counterpart of Greedy, the BST algorithm with the strongest proven and conjectured properties from the literature, widely believed to be instance-optimal. Assuming the optimality of Greedy, the smooth heap is also optimal within our model of heap algorithms. As corollaries of results known for Greedy, we obtain instance-specific upper bounds for the smooth heap, with applications in adaptive sorting. Intriguingly, the smooth heap, although derived from a non-practical BST algorithm, is simple and easy to implement (e.g. it stores no auxiliary data besides the keys and tree pointers). It can be seen as a variation on the popular pairing heap data structure, extending it with a "power-of-two-choices" type of heuristic.Comment: Presented at STOC 2018, light revision, additional figure

Оптимізація процесу роботи госпіталів

В даній бакалаврській дипломній роботі була реалізована система електронної черги з автоматичною пріоритизацією вхідного потоку пацієнтів, яка оптимізує роботу госпіталя, медичного центру, або будь-якого іншого закладу охорони здоров’я. Система дозволяє автоматизувати розподілення пацієнтів по вільним потужностям медичного закладу та формувати електронну чергу, враховуючи пріоритет кожного пацієнта, який був призначений йому при первинному огляді. Дана електрона черга надає можливість зменшити час контакту між хворими, і таким чином обмежити розповсюдження хвороби. Серверна частина цього програмного продукту була написана на мові програмування Java.In this bachelor's graduate work, an electronic queue system with automatic prioritization of the input flow of patients was implemented, which can potentially optimize the work operation of a hospital, a medical center or any other healthcare institution. The system makes it possible to automate the distribution of patients according to the free capacities of a medical institution and to form an electronic queue, taking into account the priority of each patient which was assigned to him during the initial examination. This electronic queue makes it possible to reduce the time of contact between patients and thus limit the spread of the disease. The server side of this software product was written in the Java programming language

A priority queue with the time-finger property

AbstractWe present a priority queue that supports insert in worst-case constant time, and delete-min, access-min, delete, and decrease of an element x in worst-case O(log(min{wx,qx})) time, where wx (respectively, qx) is the number of elements that were accessed after (respectively, before) the last access to x and are still in the priority queue at the time when the corresponding operation is performed. (An access to an element is accounted for by any priority-queue operation that involves this element.) Our priority queue then has both the working-set and the queueish properties; and, more strongly, it satisfies these properties in the worst-case sense. From the results in Iacono (2001) [11] and Elmasry et al. (2011) [7], our priority queue also satisfies the static-finger, static-optimality, and unified bounds. Moreover, we modify our priority queue to realize a new unifying property — the time-finger property — which encapsulates both the working-set and the queueish properties