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The amortized cost of finding the minimum [chapter]

Haim Kaplan, Or Zamir, Uri Zwick
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
More specifically, we show that for any fixed > 0, where n is the number of items in the priority queue and A(insert), A(delete) and A(find-min) are the amortized costs of the insert, delete and find-min  ...  We obtain an essentially optimal tradeoff between the amortized cost of the three basic priority queue operations insert, delete and find-min in the comparison model.  ...  Acknowledgement We would like to thank Bob Tarjan for helpful discussions and Mikkel Thorup for bringing the Brodal et al. [5] paper to our attention.  ... 
doi:10.1137/1.9781611973730.51 dblp:conf/soda/KaplanZZ15 fatcat:7chciwpzdrcatkjceybqxsmpb4

A Polylogarithmic Approximation of the Minimum Bisection

Uriel Feige, Robert Krauthgamer
2002 SIAM journal on computing (Print)  
Finding the bisection of minimum cost is NP-hard. We present an algorithm that finds a bisection whose cost is within ratio of Ç´ÐÓ ¾ Òµ from the optimal.  ...  A bisection of a graph with Ò vertices is a partition of its vertices into two sets, each of size Ò ¾. The bisection cost is the number of edges connecting the two sets.  ...  The first author is the Incumbent of the Joseph and Celia Reskin Career Development Chair. Work of the second author was supported in part by the Open University of Israel.  ... 
doi:10.1137/s0097539701387660 fatcat:mjegvxejjrcp7jqib5ioooouvq

A Polylogarithmic Approximation of the Minimum Bisection

Robert Krauthgamer, Uriel Feige
2006 SIAM Review  
It is known that finding a bisection of minimum cost is NP-hard. We present an algorithm that finds a bisection whose cost is within ratio of O(log 2 n) from the minimum.  ...  A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n/2. The bisection cost is the number of edges connecting the two sets.  ...  Acknowledgements We thank Kobbi Nissim for his part in bootstrapping this research, and the anonymous referees for comments that improved the presentation.  ... 
doi:10.1137/050640904 fatcat:vebchn4xanglve5ub2hdpso6gy

Page 682 of American Society of Civil Engineers. Collected Journals Vol. 116, Issue HY6 [page]

1990 American Society of Civil Engineers. Collected Journals  
Z* = the sum of (1) Amortized cost of installed pipe in stage tf; and (2) incremental amortized cost, for stages 1—t, of installing the stronger pressure class pipe associated with S, over that of the  ...  *, giving the minimum cost.  ... 

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.  ...  , or O( √ log log n) expected amortized cost per operation, respectively.  ...  (The analysis of [37] only showed that the extra cost is tiny.)  ... 
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.  ...  , or O( √ log log n) expected amortized cost per operation, respectively.  ...  (The analysis of [37] only showed that the extra cost is tiny.)  ... 
doi:10.1007/978-3-540-27810-8_20 fatcat:qv3yicinlrfxlmiombp5gmhkdm

Selection of a Farm Machinery Replacement Criterion Using Simulation

Darrel Kletke
1969 Southern Journal of Agricultural Economics  
The economic life of a machine is here defined as the interval of time during which that machine reaches its minimum average yearly cost.  ...  This is the same as saying that when economic life is reached, the actual yearly cost (marginal cost) is equal to the average yearly cost of the machine.  ...  This average is checked against the minimum amortized average cost of the proposed replacement.  ... 
doi:10.1017/s0081305200024249 fatcat:ti4lvbmbybg3zgqc4hpk3qfqbm

Layered Heaps [chapter]

Amr Elmasry
2004 Lecture Notes in Computer Science  
This latter priority queue achieves, in the amortized sense, constant cost per insertion, minimum finding and decrease-key operations, and logarithmic cost with at most 1.44 log n + O(log log n) comparisons  ...  In particular, we give a priority queue with constant cost per insertion and minimum finding, and logarithmic cost with at most log n + O(log log n) 1 comparisons per deletion and minimum deletion, improving  ...  This motivated the improvements in Section 4 as it appears in this version of the paper.  ... 
doi:10.1007/978-3-540-27810-8_19 fatcat:6ujxkkngpzbdhegbly5k3q2ut4

STRONGER QUICKHEAPS

GONZALO NAVARRO, RODRIGO PAREDES, PATRICIO V. POBLETE, PETER SANDERS
2011 International Journal of Foundations of Computer Science  
We prove that these offer logarithmic expected amortized complexity for all operations regardless of the input distribution.  ...  It has also been shown to offer logarithmic expected amortized complexity for all of its operations.  ...  properties assumed in the analysis of the original QHs do not hold.  ... 
doi:10.1142/s0129054111008507 fatcat:y45545cg4jbtjb63vyndlu4lmy

Maintaining Minimum Spanning Forests in Dynamic Graphs

Monika R. Henzinger, Valerie King
2001 SIAM journal on computing (Print)  
We present the first fully dynamic algorithm for maintaining a minimum spanning forest in time o( √ n) per operation.  ...  To be precise, the algorithm uses O(n 1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic.  ...  To summarize the cost of initialization when amortized over Ω(m in ) operations is O(m 1/3 in ) and the cost per deletion of an edge and finding replacement edges, when amortized over Ω(m in ) operations  ... 
doi:10.1137/s0097539797327209 fatcat:sqfj7ldpargyldr6k5o2uswoom

Page 134 of POWER Vol. 90, Issue [page]

1946 POWER  
a de- sirable minimum rate of return.  ...  Looking up intersection of 0.200 and 6° ordinates on chart find 6.2 years by inter- polating between dashed curves. This can be checked by finding the amortization rate — 0.200 — 0.060 0.140.  ... 

A potential-based amortized analysis of the union-find data structure

Gregory C. Harfst, Edward M. Reingold
2000 ACM SIGACT News  
Traditionally the amortized analysis of this structure is done using the accounting method . We present a simple, new potential-based analysis covering several of the most interestin g results.  ...  We present a simple, new potential-based amortized analysis for the standar d union-find data structure . The standard union-find data structure is simple to describe, yet has a complex analysis .  ...  Hence the amortized cost of a single find is once again O(a(m, n) ) .  ... 
doi:10.1145/356458.356463 fatcat:zajraxw7wzffpfemq6jkzhlhgu

Maintaining minimum spanning trees in dynamic graphs [chapter]

Monika R. Henzinger, Valerie King
1997 Lecture Notes in Computer Science  
We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o( √ n) per operation.  ...  To be precise, the algorithm uses O(n 1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic.  ...  To summarize the cost of initialization when amortized over (m in ) operations is O(m 1/3 in ) and the cost per deletion of an edge and finding replacement edges, when amortized over (m in )) operations  ... 
doi:10.1007/3-540-63165-8_214 fatcat:b6r3hyfduvbmraphz6xmlppddm

Fully persistent arrays [chapter]

Paul F. Dietz
1989 Lecture Notes in Computer Science  
To insert into the data structure, find the bucket whose minimum element is the greatest minimum element less than the new element, and put the new element into the bucket.  ...  If the sum of the costs of the elements of L are always O(IILII), and we assume it takes time cost(x) to relabel x, we now there is an algorithm for WMLP that takes O(I~llog IILII) amortized time for ChangeCost  ... 
doi:10.1007/3-540-51542-9_8 fatcat:6uig7nqlejaxjndlwdx4tsnucm

Pairing Heaps with Costless Meld [article]

Amr Elmasry
2009 arXiv   pre-print
Improving the structure and analysis in elm0, we give a variation of the pairing heaps that has amortized zero cost per meld (compared to an O(n) in elm0) and the same amortized bounds for all other operations  ...  More precisely, the new pairing heap requires: no cost per meld, O(1) per find-min and insert, O(n) per delete-min, and O(n) per decrease-key.  ...  find-min No potential or credit changes are required. The actual work of find-min is O(1). It follows that the worst-case cost of find-min is O(1).  ... 
arXiv:0903.4130v2 fatcat:o26mps2gyvenfkysnk625hqwiu
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