Self organising list.topic of data structure.

2.  It is a list that reorders elements based on
some self-organizing heuristics to improve
average access time.
 The simplest implementation of self-
organizing list is as a linked list.
 Being efficient in random node inserting
and memory allocation, it suffers from
inefficient accesses to random nodes.

3.  The concept of self-organizing list was
introduced by McCabe in 1965.
 In a pioneering work, he introduced two
heuristics – the MTF rule and the
transposition rule
 Further improvements were made and
algorithms suggested by Ronald Rivest,
nemes ,D Knuth and so on.

4.  The aim of this list is to improve efficiency of
linear search by moving more frequently
accessed items towards the head of the list.
 To improve average access time of nodes.

5.  THREE CASES ARE :
 AVERAGE CASE
 WORST CASE
 BEST CASE

6.  Usually, the time taken is neither the worst case time nor
the best case time
 Average case analysis assumes a probability distribution for the set of
possible inputs and gives the expected time
Tavg=1*p(1)+2*p(2)+3*p(3)+…+n*p(n)
Where p(i) is the probability of accessing the ith element in the list,also
called the access probability.
If the access probability of each element is same(i.e.
p(1)=p(2)=…..p(n)=1/n),then the ordering of the elements is irrelevant and
the average time complexity is given by:
T(n)=1/n +2/n +3/n+….n/n=(1+2+3…n)/n=(n+1)/2.

7.  T(n) doesn’t depend on the individual access
probabilities of the elements in the list in this case.
 However in the case of searches on lists with non
uniform record access probabilities, the average time
complexity can be reduced drastically by the proper
positioning of the elements contained in the list.
 This is demonstrated in the next slide.

8.  Given list:
 A(0.1), b(0.1),c(0.3),d(0.1),e(0.4)
 Without rearranging:-
 T(n)=1*0.1+2*0.1+3*0.3+4*0.1+5*0.4=3.6
 Now nodes are arranged so that the nodes with highest probability
of access are placed closest to the front.
 Now order is-> e(0.4),c(0.3),d(0.1).a(0.1),b(0.1)
 T(n)=1*0.4+2*0.3+3*0.1+4*0.1+5*0.1=2.2
 Thus the average time required for searching in an organized list is
very less than the time required to search a randomly arranged list.

9. WORST CASE:
In this case, the element Is located at the very end of list,be
it a normal list or a self-organized list and thus n
comparisons must be made to reach it.
BEST CASE:
In the best case, the element to be searched is one which has
been commonly accessed and has thus been identified by
the list and kept at the head.

11.  MOVE TO FRONT(MTF)
 TRANSPOSE
 COUNT
 ORDERING

12.  This technique moves the element which is
accessed to the head of the list.
 This has the advantage of being easily
implemented and requiring no extra memory.
 This heuristic also adapts quickly to rapid
changes in the query distribution.

14.  This technique involves swapping an
accessed node with its predecessor.
 Therefore, if any node is accessed, it is
swapped with the node in front unless it is the
head node, thereby increasing its priority.
 This algorithm is again easy to implement
and space efficient and is more likely to keep
frequently accessed nodes at the front of the
list.

16.  In this technique, the number of times each
node was searched for is counted i.e. every
node keeps a separate counter variable which
is incremented every time it is called.
 The nodes are then rearranged according to
decreasing count.
 Thus, the nodes of highest count i.e. most
frequently accessed are kept at the head of
the list.

18.  This technique orders a list with a particular
criterion.
 For e.g in a list with nodes 2,3,7,10.
 If we want to access node 5, then the
accessed node is added between 3 and 7 to
maintain the order of the list i.e. increasing
order.

19. In the first three techniques i.e. move to
front, transpose and count ,node is added
at the end whereas in the ordering
technique , node is added somewhere to
maintain the order of the list.

21. 21

22. An inversion is defined to be a pair of elements
(x,y) such that in one of the lists x precedes y and
in the other list y precedes x. For example, the list
[C, B, D, A] has four inversions with respect to the
list [A, B, C, D], which are: (C,A), (B,A), (D,A), and
(C,B). The amortized cost is defined to be the sum
of the actual cost and the difference between the
number of inversions before accessing an element
and after accessing it,
amCost(x) = cost(x) + (inversionsBefore Access(x) –
inversionsAfterAccess(x))

23.  Language translators like compilers and interpreters use self-
organizing lists to maintain symbol tables during compilation
or interpretation of program source code.
 Currently research is underway to incorporate the self-
organizing list data structure in embedded systems to reduce
bus transition activity which leads to power dissipation in
some circuits.
 These lists are also used in artificial intelligence and neural
networks as well as self-adjusting programs.
 The algorithms used in self-organizing lists are also used as
caching algorithms as in the case of LFU algorithm.

24.  Given a set of search data, the optimal static
ordering organizes the records precisely
according to the frequency of their
occurrence in search data.The frequency
count and MTF technique in the long run are
twice as costly as optimal static ordering and
count technique approaches the cost of MTF
technique.Although this can be imprecise as
it depends on the data.