Data Structures and Algorithms Lecture Notes

16 February 2011 • Odds and Ends

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Outline

• Storage management.
  • Delayed storage recovery.
  • Free lists.
• Another array-based linked-list data types.
• Other linked-list operations.

A Dynamic-Array Pathology

• Frequently crossing the same resize point causes highly inefficient execution.

Adding Delay

• Don’t immediately resize, delay until sure.
  • Delay is asymetric: expansion can’t be delayed.
• Define a low-water mark below the resize point.

  

  • Delay contraction while the data-type size is above the low-water mark.

Delay Example

Reduction point: n/2 Low-water mark: 1 below reduction

Controlling Delay

• Delay can be specfied as a percentage (p% below the resize point) or absolutely (a elements below the resize point).
• The client can set the delay, or the data type can, or they both can.
  • Clients know more about their application, but get things wrong and may not recognize the problem.
  • The data type is always aware of the problem, but may not know the best way to solve it.

Dynamic Linked Sequences

void addAfter(T v) Node n = new Node() n.value = v n.next = next next = n
void remove(T v) Node l = findBefore(v) l.next = l.next.next

• The boxed code creates nodes and garbage (unreferenced instances).

Dynamic Storage Costs

• Creating new nodes and collecting garbage is expensive.
  • Although dynamic-storage managers have gotten good at their job.
• Large linked lists with much turnover may have high storage-management costs.
  • Leading to slow and bloaty code.
• What can be done to reduce storage-management costs?

Free Lists

• The usual solution to garbage problems is recycling.
  • Move unlinked nodes to a free list; they’re not garbage any more.
  • Check the free list before allocating new nodes.

  

Free-List Management

private Node newNode() if freeList != null Node n = freeList freeList = n.next return n return new Node()
public void remove(T v) Node n = findBefore(v) Node l = n.next n.next = l.next l.next = freeList freeList = l

Oh Really?

• Generate 100,000 pairs of adds and removes.
• Each pair is some number of adds followed some number of removes.
  • Add runs are (rand(10) + 1)*10 long.
  • Remove runs are rand(ll.size()) + 1 long.
• The operation sequence looks like

  put() put() … get() get() put() … get() …

Results

• Java 1.6.17 on an elderly single-core laptop.
  • No compiler or JVM command-line options.
• Free-list manged code runs 1.8 to 2 times faster than new + garbage-collected code.
  • Ten-run average: 1.9, 0.02 std dev.
• Same set-up, but with Java 1.6.21:
  • Ten-run average: 1.1, 0.003 std dev.
  See the the code; see an example run.

Free-List Problems.

• If linked-list size is bimodal (large and small), the free list may have too many unused links.
  • Similar to large mostly empty arrays, and handled in the same way.
  • Throw some fraction of the free list on the floor.
• If the linked-list size is constantly changing, the free list may thrash.
  • Use a low-water mark to make sure the linked-list size is stably small.

Free-List Problems..

• If free-list links continue to reference values, they may obstruct value garbage collection.

  

• Null out the value field(s) when hanging a link on the free list.

Dynamic-Array Lists

• Using a dynamic array gives dynamic linked lists.
• But dynamic arrays won’t do anything about slow add and removes.
  • Values in the array still have to be moved around.
• How can dynamic arrays be used to provide fast adding and removing?

Faster Array Linked Lists

• values[i] is the value stored in link i.
• next[i] is the index to link i’s successor.

Link Definition

class Link<T> {
  T value;    // values[i]
  Link next;  // next[i]
  }

Example

• A dynamic linked list:

  

• The equivalent linked array implementation:

  

Link Allocation

• An n-element array defines n links.

  

• A free link can have an invalid next value, such as -1.
• Free-link allocation searches for a link with an invalid next value.
  • Is there a better way?

Free Lists Again

• Thread the free links onto a free list for fast free-link allocation.

  

Linked-List Comparison

	List	List	List
	(Array)	(LArray)	(Node)
create	fast	fast	fast
delete	fast	fast	fast
add	slow	fast	fast
remove	slow	fast	fast
traversal	fast	fast	fast
navigation	fast	slow	slow
dynamic	no	no	yes

• fast: single-element operation.
  slow: potentially n-element operation.

Summary

• Expensive operations should not be performed frequently.
  • Make them less expensive or less frequent if they are.
• Spread an operation’s cost over as many payers as possible.
  • Recycle your garbage.
• Explicit adjacency relations allow fast value manipulations, even in arrays.

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This page last modified on 2010 October 12.