Approaches

Nbr and list of parameters

Functions

Output

Structure

Technics

Constraints

Greedy algorithm

3

$V=\left\{v_1,v_2,\cdots ,v_n\right\}$ Set of candidate view, $C=\left\{c_1,c_2,\cdots ,c_n\right\}$ where c_i as the associated size of each view candidate v_i

K: number max of view to be materialized,

$\max \left(B\left(v,S\right)\right)=\max \left({\displaystyle {\sum }_{W\le U}{B}_W}\right)$

S: Subset of materialized views with Max(B(v, S))

Data cube lattice

Select a Subset S of k views v including a top view where the benefit B(v, S) is maximized. For each view u relative to S calculate $B\left(v,S\right)={\displaystyle {\sum }_{W\le U}{B}_W}$ .

Where w is all descending of u.

K: number max of view to be materialized

Greedy Genetic Algorithm

6

lattice of N Cubes $C=\left\{c_1,c_2,\cdots ,c_i,\cdots ,c_n\right\}$ , A Set of Query $Q=\left\{q_1,q_2,\cdots ,q_i,\cdots ,q_k\right\}$ , Frequency Values for each query $F=\left\{f{q}_1,f{q}_2,\cdots ,f{q}_i,\cdots ,f{q}_k\right\}$ , Update Frequency of cubes $G=\left\{g{c}_1,g{c}_2,\cdots ,g{c}_i,\cdots ,g{c}_n\right\}$ , Constraint Space S.

$\begin{array}{l}\mu (·)={\displaystyle {\sum }_{i=1}^{k}f{q}_{i}E\left(q_i,M\right)}\\ +{\displaystyle {\sum }_{c\in M}gcU\left(c,M\right)}\end{array}$

ῼ = (L, C, R, Q, F, G, S)

Data cube lattice

Genetic Greedy Method.

Storage Space, ${\displaystyle {\sum }_{c\in Mc}\left|c\right|}\le S$

Genetic Algorithm

4

Lattice of Views with size of each view, P_c: Probability of crossover,

P_m: Probability of mutation, G: Pre-defined number of generations.

$\begin{array}{l}TVEC={\displaystyle {\sum }_{i=1\wedge SMvi=1}^{N}Size\left(Vi\right)}\\ +{\displaystyle {\sum }_{i=1\wedge SMvi=0}^{N}SizeSMA\left(Vi\right)}\end{array}$

Top-T Views.

Data cube lattice

Genetic method.

G: Number of generations

A Distributed Clustering with Intelligent Multi Agents System

1

Queries workload.

$DIC=\frac{{\displaystyle {\sum }_{i=1}^{j=k}Dist\left(O_j,O_i\right)}}{K}$

$\begin{array}{l}Dist\left(O_j,O_i\right)\\ ={\displaystyle \sum _{k=1}^m\left|M\left(O_i,q_k\right)-M\left(O_j,q_k\right)\right|}\end{array}$

Cluster with configuration provide minimal queries cost.

NONE

Generates a predicates usage matrix M with row presented by all queries and column defined by the restriction predicate and joint predicate. Use a distributed clustering based on k-means algorithm created and managed by COA. Each COA responsible of set of Cluster Agents (CAs).

Storage Space, MinDist.

Clustering technique

3

Set of relation: $R\left(A_1,A_2,\cdots ,A_m\right)$ ;

The set of queries: $Q=\left\{Q_1,Q_2,\cdots ,Q_n\right\}$

Average Similarity: cut-off:.

$\begin{array}{l}TVEC={\displaystyle {\sum }_{i=1\wedge SMvi=1}^{N}Size\left(Vi\right)}\\ +{\displaystyle {\sum }_{i=1\wedge SMvi=0}^{N}SizeSMA\left(Vi\right)}\end{array}$

Cluster of materialized views

NONE

Construct Attribute Usage Matrix M attributes * N queries. Generate Attribute Similarity Matrix M * M between attributes. Calculate similarity by

$Jaccard\left(A,B\right)=\frac{\left|A\right|\cap \left|B\right|}{\left|A\right|\cup \left|B\right|}$

J(A_i, A_j) = J(A_j, A_k) ≥ cut-off. So

Particle Swarm Optimization Algorithm (PSO)

6

lattice of N Cubes $C=\left\{c_1,c_2,\cdots ,c_i,\cdots ,c_n\right\}$ , A Set of Query $Q=\left\{q_1,q_2,\cdots ,q_i,\cdots ,q_k\right\}$ , Frequency Values for each query $F=\left\{f{q}_1,f{q}_2,\cdots ,f{q}_i,\cdots ,f{q}_k\right\}$ , Update Frequency of cubes, cube invoking frequency $CF=\left(f{c}_1,f{c}_2,\cdots ,f{c}_n\right)$ , Constraint Space S.

$fm=\min \left({\displaystyle {\sum }_{i=1}^{k}f{q}_{i}E\left(q_i,M\right)}\right)$

Binary string of length n bits [0, 1] witch is set of Cubes M to minimizing fm

Data cube lattice

Genetic Algorithm. Particle Swarm Optimization Algorithm

Storage Space ${\displaystyle {\sum }_{c\in Mc}\left|c\right|}\le S$

coral reefs optimization algorithm (CROMVS)

8

MVPP, K = Number of generating populations, M = Number of Queries, N = Number of Relations, H = threshold times, F_a = Fraction of asexual reproduction, F_b = Ratio of number of selected solutions, F_d = Fraction of the worst solutions

$\begin{array}{l}{f}_x={\displaystyle {\sum }_{i\in M}\left({\displaystyle {\sum }_{q\in Q}e{f}_q\ast C_i^q}\right)}\\ -({\displaystyle {\sum }_{u\in Prej\cap x}{\displaystyle {\sum }_{q\in Q}e{f}_q\ast C_u^q}}\\ +{\displaystyle {\sum }_{r\in R}u{f}_r\ast C_i^r})\end{array}$

MV with MAX(f_x)

MVPP

Coral reefs algorithm, is Meta-heuristic algorithm based on coral reproduction and coral reefs formation which performed using: external sexual reproduction, internal sexual reproduction, and asexual reproduction

Population List with Max(f_x)

Multi- Objective MONPGA.

5

L: Size of each view, P_c: probability of crossover, P_m: probability of mutation, K: number of views to be selected and G: the maximum number of generations

$TVEC\left(V_{Top\text{-}k}\right)=C_{MV}+C_{NMV}$

Top-K views TKV

Data cube lattice

Genetic Algorithm.

K: number of views to be selected and G: the maximum number of generations

A game theory-based framework (GTMVS)

4

$R=\left\{R_1,R_2,\cdots ,R_r\right\}$ : Set of base relations

uf_i: update frequency for R_i.

$Q=\left\{Q_1,Q_2,\cdots ,Q_q\right\}$ : Set of queries, ef_i execution frequency for Q_i.

$\begin{array}{l}{g}_x={\displaystyle {\sum }_{i\in M}({\displaystyle {\sum }_{r\in R}u{f}_r\ast C_i^r}}\\ +{\displaystyle {\sum }_{q\in Q}e{f}_q\ast C_i^q})\end{array}$

select the optimal set $M=\left\{M_1,M_2,\cdots ,M_m\right\}$ with lowest cost represented by both sets of player1 and player2.

MVPP

Game theory who the Players of game are: Query processing cost and view maintenance cost. Player strategy used TSGV. [35]

M: list of nodes in MVPP-Player 1 union Player 2. materialized view List

Map-Reduce model (MR-MVPP)

7

Q: workload of queries

f_q: list of query frequencies

R: base relations

f_u: list of update frequencies

b: number of categories

A: a number between 0 and 1 for hash function

t: threshold of similarity

$Q{C}_i=f_{qi}\ast {\displaystyle {\sum }_{\left\{j|Q_i\in Query\left(V_j\right)\right\}}ACost\left(V_j\right)}$

MVPP that has the least total cost.

MVPP

The map-reduce programming

Model; The hashing technique; Use 4 algorithms. are: MR-MVPP, SSJoin, map, and reduce. Calculate similarity by Jaccard Function.

$Jaccard\left(A,B\right)=\frac{\left|A\right|\cap \left|B\right|}{\left|A\right|\cup \left|B\right|}$

MVPP with least total cost = Min(QC_i)