T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 107

Esponda et al. (2006) proposed a distributed NDB model, which not only
fi xed some properties of the monolithic database but also created some new ones of
its own. h e main disadvantage of the model is the size of the database. Because
one database stores one record, the size of the composite database grows as a linear
function of the number of positive records.

4.9.4 Operations on Negative Database

Basic database operations such as initialization, insertion, and deletion are used
to describe the NDB. h e proposed algorithms for these operations may cause the
size of the NDB to grow unreasonably. It is important for any implementation to
control the number of entries that match a particular string. Some operations can
be described as follows (Esponda et al., 2006):

Insert operation . h ere are two inputs for this operation: NDB and the string x
(to be inserted) and outputs an NDB

′

database that matches every string
matched by NDB and every string matched by x .
Delete operation. h ere are two inputs for this operation: NDB and the string x
(to be inserted) and outputs an NDB database that matches every string

matched by NDB and removes every string matched by x .
Morph operation. h is operation takes NDB as input and outputs NDB

′

′ of same

′

binary string but both NDB and NDB are diff erent as some records of NDB

are not in NDB and vice versa. h is allows NDBs to have in diff erent repre-

sentations for the same data.

′

4.9.4.1 Negative Algebra

h ere are many algebraic operations for NDB such as relational algebra opera-
tions for sets. h ese operations include negative select, negative union, cartesian
product, join and intersection, negative cartesian product, and negative join.
Some of these operations are described as follows (see Esponda et al., 2007b for
details):

_ ). h is is just the opposite of the intersection operation
on the sets, that is, this operation uses De Morgan's law and will union the
elements of both the NDB (Esponda et al., 2007b). h e negative intersection
can be defi ned as follows:

Negative intersection (

NDB NDB ∩ NDB { xx ∈ NDB } ∪ { y y ∈ NDB }

3 1 2 1 2

- ).

∩

Table 4.6 illustrates the example of negative intersection (

− ). h is operation is opposite of the intersection operation
for sets, where only those strings or records which are common to both

Negative union (