PRIORITY QUEUES

1
PRIORITY QUEUES SORTING METHODS FOR PARALLEL
SIMULATION

• Authors
• Miltos D.Grammatikakis Stefan Liesch
• Citation
• IEEE Transactions On Software Engineering,
  Volume 26, No.5, May 2000

2
Overview

• Introduction
• Distributed Priority Queues
• Concurrent Priority Queues
• Dynamically Balanced Concurrent
• Priority Queues
• Experiments
• Conclusions
• Futurework

3
Introduction

• A Review on
• Sequential Priority Queues
  (Heap Implementation)
• Previous Parallel Implementations
• Goal Of the Paper
• Applications

4
Sequential Priority Queues

• Implementation using Heaps
• Fast Ideally Suited

5
Min-Heap Properties

• Values Stored at any Node
• Always Less than or Equal to Values
• Stored at Both Child Nodes
• All Levels Except the Last Have to be Completely
  Filled

6
An Example Inserting in a Min -Heap

• Start at a New Leaf Node
• To maintain the binary trees completeness
• Percolate the New Element up to its Appropriate
  Position
• To maintain the heap order property

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An Example Inserting in a Min -Heap
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An Example Inserting in a Min -Heap
12
9
An Example Inserting in a Min -Heap
10
17
13
12
30
25
31
45
61
58
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10
An Example Inserting in a Min -Heap
10
17
12
13
30
25
31
45
61
58
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15
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An Example Deleting in a Min -Heap

• Remove the Minimum Element at Root, Detach the
  Rightmost Element From the Bottom Level
• If It has Highest Priority,Insert at Root
• Deletion Complete.
• Otherwise Perform Heapification

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An Example Deleting in a Min -Heap
Highest Priority Element
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An Example Deleting in a Min -Heap
Delete Minimum Element
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An Example Deleting in a Min -Heap
43
51
63
77
58
65
91
73
75
87
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Remove Check
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An Example Deleting in a Min -Heap
An Example Deleting in a Min -Heap
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Smaller Child
51
63
77
58
65
91
73
75
87
80
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An Example Deleting in a Min -Heap
43
58
51
Smaller Child
63
77
65
91
73
75
87
80
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An Example Deleting in a Min -Heap
An Example Deleting in a Min -Heap
43
58
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Last Element Fits Here
63
77
73
65
91
75
87
80
18
Previous Implementations of PQ

• Sequential Priority Queues
• Parallel Priority Queues
• Distributed Priority Queues ( DPQ )
• Concurrent Priority Queues ( CPQ )

19
Goal Of the Paper

• To propose a new concurrent data structure based
  on distributed circular sorted lists,
• known as
• a Balanced Concurrent
• Priority Queue( BCPQ )
• and perform comparisons of previous
  implementations with this structure on a common
  parallel platform

20
Some Applications

• Parallel Algorithms for Decision Making in
  Finance or Games
• Kruscals Graph Algorithm in Network Design
• Dijkstras Algorithm for the Shortest Path Problem

• Heuristics for NP Complete Problems
• For Processing Signs based on relative
  significance in Pattern Recognition
• Job Event Schedulers in Operating Systems

21
Previous Parallel PQ Implementations

• Distributed Priority Queues ( DPQ )
• O ( log P log N )
• Concurrent Priority Queue ( CPQ )
• O ( log N/P )

22
Distributed Priority Queue (DPQ)

• A Distributed Data Structure ( Heap )
• Elements Stored at Each Processor have Higher
  Priorities Than Those Stored at Their Children
• Centralised Control
• ADT Operations Start at Root Processor
• Step For Generating Round Robin Sequence
• Each Node Consists of Splay Trees of Items

23
The DPQ Structure as a Binary Heap
Splay trees
1
2
3
1
6
7
4
5
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DPQInsert Operation

• Send the Item to the Root Processor
• Tranfer Control to The Root Processor
• Root Computes the Position P of the Future Host
  Processor,
• Selects the Appropriate Path and Initiates the
  Insertion Along the Path.
• Heap Property Maintained

• Send the Item to the Root Processor
• Tranfer Control to The Root Processor
• Root Computes the Position P of the Future Host
  Processor,
• Selects the Appropriate Path and Initiates the
  Insertion Along the Path.
• Heap Property Maintained

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DPQDeleteMin Operation

• Root Immediately Sends Back Its Minimum Value
  Item.
• Gets Next Priority Item from Child Processor.
• Performs Reheapification.
• If DPQ Empty
• Stores the Number of the Requesting Processor in
  the Waiting List.
• The Item of The Next Incoming Insert Query Is
  Sent Immediately to the First Waiting Processor.

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DPQ MPI Implementation

• http//members.aol.com/liesche/darbeit.zip

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Concurrent Priority Queue (CPQ)

• Binary Heap, Uniform Shared Memory
• Mutual Exclusion Locks on Each Node of Heap
• Mutual Exclusion Lock on a Variable that holds
  the Number of Items in the Heap
• Items are Tagged
• Empty Valid Transient ( pid )
• Consecutive Inserts Deletes Traverse Disjoint
  Paths to the Root

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The CPQ Data Structure
15
t tag d data
0001
87
311
0010
0011
350
380
275
703
0111
0100
0101
0110
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CPQInsert Operation

• New Item Stored in a Free Node
• Moved up Level by Level
• During Each Move
• Parent Child Node Locked
• Item Priorities Compared
• If Child has higher priority, items are swapped
• Both Locks Are Released
• New Item Climbs up till Heap Condition Restored

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CPQDeleteMin Operation

• Exchange item Last Stored at last heap leaf with
  item at root
• Corresponding Nodes are Locked
• Last Node tagged empty, Lock released
• Root Node remains Locked
• Heapification Done with Node holding Last kept
  locked
• After Last stops Moving DeleteMin Stopped Lock
  of Last is Released

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CPQShMem Implementation

• Details
• http//members.aol.com/liesche/darbeit.zip

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Dynamically Balanced Concurrent Priority Queue
(BCPQ)

• Each Processor Stores Part of the List in a
  Circular Queue
• Single Lock
• Processor 1 Stores Items with Highest Priority
• Subsequent Items Stored at Processor 2,3,4..P
• Load Balancing

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The BCPQ Data Structure
lock
8 9 5 6 7
N-2 N-1 N
1 2 3
4
30
32
4
7
8
14 17
25
84
89
75
12
tail
head
. . . . . . . . . .
Pr 2
Pr 1
Pr P
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BCPQInsert Operation

• Binary Search For Local List on which New Item to
  be inserted
• Lock list m
• Compare Priorities
• Release Lock
• Continue till Target List found
• Second Binary Search for Target Position within
  Target List

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BCPQDeleteMin Operation

• Lock List 0
• Return Minimum Item
• Release Lock
• If List Empty, Go to Next List
• Continue till Minimum Item Found

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BCPQ

• O ( N / P ) Complexity
• After Optimization 5 faster than CPQ

37
Experiments

• Based on a Cray-T3E900 system with
• 32 Processing Elements
• Involved
• Parallel Simulations of Single Buffers,
• a 64X64 Packet Switch ( with multicasting )
• Symmetric Networks

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Conclusions

• CPQ BCPQ
• easy to use
• 5 -10 times faster than DPQ
• BCPQ
• performance comparable to CPQ
• more efficient in assigning memory than
  CPQ

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Conclusions

• Reduced Sorting Overheads
• Minimized Interprocessor Communications
• Optimized Scalar Processing
• Achieved Good Scalability Efficiency

40
Extensions Futurework

• Further Reduce
• Communication Overhead
• Transform the BCPQ to be Lock Free
• Further Improve BCPQ to Achieve Platform Wide
  Portability using MPI-2

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Questions ?