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Melding priority queues

Ran Mendelson, Robert E. Tarjan, Mikkel Thorup, Uri Zwick
2006 ACM Transactions on Algorithms  
into a priority queue data structure that also supports fast meld operations with essentially no increase in the amortized cost of the other operations.  ...  Priority queues are basic data structures used by many algorithms.  ...  Concluding remarks We presented an improved analysis of a general transformation, first presented in van Emde Boas [37] , that adds a meld operation to priority queue data structures that do not support  ... 
doi:10.1145/1198513.1198517 fatcat:ox4auyefabcivepe4cnnoa33ma

Melding Priority Queues [chapter]

Ran Mendelson, Robert E. Tarjan, Mikkel Thorup, Uri Zwick
2004 Lecture Notes in Computer Science  
into a priority queue data structure that also supports fast meld operations with essentially no increase in the amortized cost of the other operations.  ...  Priority queues are basic data structures used by many algorithms.  ...  Concluding remarks We presented an improved analysis of a general transformation, first presented in van Emde Boas [37] , that adds a meld operation to priority queue data structures that do not support  ... 
doi:10.1007/978-3-540-27810-8_20 fatcat:qv3yicinlrfxlmiombp5gmhkdm

Fast Meldable Priority Queues

Gerth Stølting Brodal
1995 BRICS Report Series  
<br />To our knowledge this is the first priority queue implementation that<br />supports Meld in worst case constant time and DeleteMin in logarithmic<br />time.  ...  We present priority queues that support the operations MakeQueue,<br />FindMin, Insert and Meld in worst case time O(1) and Delete and<br />DeleteMin in worst case time O(log n).  ...  Then join the n priority queues to one priority queue by n−1 Meld operations. The Meld operations are done bottom-up by always melding two priority queues of smallest size.  ... 
doi:10.7146/brics.v2i12.19515 fatcat:dxsmuwetabfvfebajaisjcfply

Fast meldable priority queues [chapter]

Gerth Stølting Brodal
1995 Lecture Notes in Computer Science  
We present priority queues that support the operations MakeQueue, FindMin, Insert and Meld in worst case time O(1) and Delete and DeleteMin in worst case time O(log n).  ...  The time bounds are optimal for all implementations where Meld takes worst case time o(n).  ...  Then join the n priority queues to one priority queue by n−1 Meld operations. The Meld operations are done bottom-up by always melding two priority queues of smallest size.  ... 
doi:10.1007/3-540-60220-8_70 fatcat:iaau75pvyzhjrie2roitruncyi

Functional Binomial Queues [chapter]

David J. King
1995 Functional Programming, Glasgow 1994  
E cient implementations of priority queues can often be clumsy beasts. We express a functional implementation of binomial queues which is both elegant and e cient.  ...  priority queues.  ...  For example, the correctness of the meld function is shown by p r o ving: 8p q: isBinQ p^isBinQ q ) isBinQ (meld p q ) Now w e can start to express the priority queue operations.  ... 
doi:10.1007/978-1-4471-3573-9_10 dblp:conf/fp/King94 fatcat:zvowcsrmgbaa3pcq5giqkoqfzi

Optimal Purely Functional Priority Queues

Gerth Stølting Brodal, Chris Okasaki
1996 BRICS Report Series  
the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other<br />priority  ...  Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worst-case time, and deleteMin in O(log n) worst-case time.  ...  The basic idea is to reduce melding to simple insertion by using priority queues that contain other priority queues.  ... 
doi:10.7146/brics.v3i37.20019 fatcat:ebvsdo4zxngnhbhooruumouffe

Optimal purely functional priority queues

Gerth Stølting Brodal, Chris Okasaki
1996 Journal of functional programming  
running time offindMintoO(1) by adding a global root to hold the minimum element; and finally, we reduce the running time ofmeldtoO(1) by allowing priority queues to contain other priority queues.  ...  These bounds are asymptotically optimal among all comparison-based priority queues. In this paper, we adapt Brodal's data structure to a purely functional setting.  ...  The basic idea is to reduce melding to simple insertion by using priority queues that contain other priority queues.  ... 
doi:10.1017/s095679680000201x fatcat:bcluocodrrcmhn6j255l7egave

A Survey on Priority Queues [chapter]

Gerth Stølting Brodal
2013 Lecture Notes in Computer Science  
Since then numerous papers have been published on priority queues. This paper tries to list some of the directions research on priority queues has taken the last 50 years.  ...  Back in 1964 Williams introduced the binary heap as a basic priority queue data structure supporting the operations Insert and Ex-tractMin in logarithmic time.  ...  The first priority queue with worst-case o(lg n) time Meld was a generalization of binomial queues by Fagerberg [63] , supporting Meld in o(lg n) time and ExtractMin in time ω(lg n).  ... 
doi:10.1007/978-3-642-40273-9_11 fatcat:zocxhiyfmvdgzn2yoob25h3wr4

Priority queues on parallel machines

G.S. Brodal
1999 Parallel Computing  
On a processor array of size O(log n) each of the operations Make-Queue, Insert, Meld, FindMin, ExtractMin, Delete and Decrease-Key can be supported in constant time.  ...  MakeQueue Creates and returns a new empty priority queue. Insert(Q; e) Inserts element e into priority queue Q. Meld(Q 1 ; Q 2 ) Melds priority queues Q 1 and Q 2 .  ...  On a CREW PRAM priority queues exist supporting FindMin in constant time with one processor, and MakeQueue, Insert, Meld and In this section we extend the repertoire of supported priority queue operations  ... 
doi:10.1016/s0167-8191(99)00032-0 fatcat:z7o4v5jeqzecdig7khrowcnjfe

Simulation Analysis of a Liver Transplantation Queueing System

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
Depending on the blood group and MELD score, the priority is given to the waiting patients.  ...  Patients with MELD score 6-30 can join in the low priority queue of infinite capacity whereas patients with high MELD score (30-40) should join the high priority queue of limited capacity.  ...  Here we classify the queue into two types. People with high risk that is with MELD score of 30 to 40 is made to wait in a high priority queue, where as remaining people wait in a low priority queue.  ... 
doi:10.35940/ijitee.a4149.119119 fatcat:mrfgpph5lrftlint3bfh6hllwa

Priority queues on parallel machines [chapter]

Gerth Stølting Brodal
1996 Lecture Notes in Computer Science  
We present time and work optimal priority queues for the CREW PRAM, supporting FindMin in constant time with one processor and MakeQueue, Insert, Meld, FindMin, ExtractMin, Delete and DecreaseKey in constant  ...  A pipelined version of the priority queues adopt to a processor array of size O(log n), supporting the operations MakeQueue, Insert, Meld, FindMin, ExtractMin, Delete and DecreaseKey in constant time.  ...  MakeQueue Creates and returns a new empty priority queue. Insert(Q; e) Inserts element e into priority queue Q. Meld(Q 1 ; Q 2 ) Melds priority queues Q 1 and Q 2 .  ... 
doi:10.1007/3-540-61422-2_150 fatcat:c4gt3sefmzfjvdey2vwtsxusiy

Two new methods for constructing double-ended priority queues from priority queues

Amr Elmasry, Claus Jensen, Jyrki Katajainen
2008 Computing  
We introduce two data-structural transformations to construct doubleended priority queues from priority queues.  ...  To apply our transformations the priority queues exploited must support the extraction of an unspecified element, in addition to the standard priority-queue operations.  ...  Note that, even if the priority queues are meldable, the resulting double-ended priority queue cannot provide meld efficiently.  ... 
doi:10.1007/s00607-008-0019-2 fatcat:tym6ges4yjgpzoa3a5wxtw5kdu

A generalization of binomial queues

Rolf Fagerberg
1996 Information Processing Letters  
Examples include the rst priority queue to combine a sub-logarithmic worst case bound for Meld with a sub-linear worst case bound for Delete min.  ...  Di erent sequences lead to di erent w orst case bounds for the priority queue operations, allowing the user to adapt the data structure to the needs of a speci c application.  ...  In meldable priority queues, the basic operations are insertion of a new element i n to a queue, deletion of the element h a ving minimum key in a queue, and melding of two queues into a single queue.  ... 
doi:10.1016/0020-0190(95)00194-8 fatcat:chvvye7buffu7bn2ozjh5wklci

Worst-Case Optimal Priority Queues via Extended Regular Counters [article]

Amr Elmasry, Jyrki Katajainen
2011 arXiv   pre-print
We consider the classical problem of representing a collection of priority queues under the operations , , , , , and .  ...  Brodal showed that his worst-case efficient priority queues achieve these worst-case bounds. Unfortunately, this data structure is involved and the time bounds hide large constants.  ...  Brodal for taking the time to explain some details of his construction, and Claus Jensen for reviewing this manuscript and teaming up with us for six years in our research on the comparison complexity of priority-queue  ... 
arXiv:1112.0993v1 fatcat:xogofnn27rfmrbl3dagznl7eqa

A simpler implementation and analysis of Chazelle's Soft Heaps [chapter]

Haim Kaplan, Uri Zwick
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
Chazelle's soft heaps are derived from the binomial heaps data structure in which each priority queue is composed of a collection of binomial trees.  ...  We describe a simpler and more direct implementation of soft heaps in which each priority queue is composed of a collection of standard binary trees.  ...  The meld operation A meld(P, Q) operation receives two priority queues P and Q and returns a new priority queue obtained by melding P and Q. Melding P and Q is done in a fairly straightforward way.  ... 
doi:10.1137/1.9781611973068.53 fatcat:d4vfuz3nmjhojpbrgnsbq4uz2u
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