A Tale Of Two Simple Data Structures

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A Tale Of Two Simple Data Structures

• Free, We Lunch

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• It was the best of times, it was the worst of
  times, it was the age of wisdom, it was the age
  of foolishness, it was the epoch of belief, it
  was the epoch of incredulity, it was the season
  of Light, it was the season of Darkness, it was
  the spring of hope, it was the winter of despair,
  we had everything before us, we had nothing
  before us, we were all going direct to Heaven, we
  were all going direct the other way . . .

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Fat Heaps

• Meldable Heaps and Boolean Union-FindKaplan,
  Shafrir, TarjanSTOC 2002
• New Heap Data StructuresKaplan, Tarjan1998

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Binary Williams 64 Floyd 64
Binomial Vuillemin 78
LeftistCrane 72
Post OrderHarvey Zatloukal 04
VPeterson 87
Fibonacci Fredman Tarjan 87
SkewSleator Tarjan 86
Brodal 95
Relaxed 2Driscoll 88
Relaxed FibonacciBoyapati 95
Brodal Okasaki 95
Thin and FatKaplan Tarjan 98
PairingFredman 86
Brodal 96
SoftChazelle 00
FishspearFischer Paterson 94
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Meldable Heap Interface
Fat Fibonacci
MakeHeap() O(1) O(1)
FindMin(h) O(1) O(1)
Insert(h, x) O(1) O(1)
DecreaseKey(h, x, ?) O(1) O(1)
DeleteMin(h) O(log n) O(log n)
Meld(h1, h2) O(log n) O(1)
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Parallel Algorithms
time
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Redundant Counters

• We want to be able to add 1 to an arbitrary digit
  of a number in worst-case O(1) time.

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Let