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 ci as the associated size of each view candidate vi K: number max of view to be materialized, $\mathrm{max}\left(B\left(v,S\right)\right)=\mathrm{max}\left({\sum }_{W\le U}{B}_{W}\right)$ 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 $B\left(v,S\right)={\sum }_{W\le U}{B}_{W}$ . 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. $\begin{array}{l}\mu \left(·\right)={\sum }_{i=1}^{k}f{q}_{i}E\left({q}_{i},M\right)\\ +{\sum }_{c\in M}gcU\left(c,M\right)\end{array}$ ῼ = (L, C, R, Q, F, G, S) Data cube lattice Genetic Greedy Method. Storage Space, ${\sum }_{c\in Mc}|c|\le S$ Genetic Algorithm 4 Lattice of Views with size of each view, Pc: Probability of crossover, Pm: Probability of mutation, G: Pre-defined number of generations. $\begin{array}{l}TVEC={\sum }_{i=1\wedge SMvi=1}^{N}Size\left(Vi\right)\\ +{\sum }_{i=1\wedge SMvi=0}^{N}SizeSMA\left(Vi\right)\end{array}$ Top-T Views. Data cube lattice Genetic method. G: Number of generations A Distributed Clustering with Intelligent Multi Agents System 1 Queries workload. $DIC=\frac{{\sum }_{i=1}^{j=k}Dist\left({O}_{j},{O}_{i}\right)}{K}$ $\begin{array}{l}Dist\left({O}_{j},{O}_{i}\right)\\ =\sum _{k=1}^{m}|M\left({O}_{i},{q}_{k}\right)-M\left({O}_{j},{q}_{k}\right)|\end{array}$ 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: $Q\text{}=\left\{{Q}_{1},{Q}_{2},\cdots ,{Q}_{n}\right\}$ Average Similarity: cut-off:. $\begin{array}{l}TVEC={\sum }_{i=1\wedge SMvi=1}^{N}Size\left(Vi\right)\\ +{\sum }_{i=1\wedge SMvi=0}^{N}SizeSMA\left(Vi\right)\end{array}$ Cluster of materialized views NONE Construct Attribute Usage Matrix M attributes * N queries. Generate Attribute Similarity Matrix M * M between attributes. Calculate similarity by $Jaccard\left(A,B\right)=\frac{|A|\cap |B|}{|A|\cup |B|}$ J(Ai, Aj) = J(Aj, Ak) ≥ 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. $fm=\mathrm{min}\left({\sum }_{i=1}^{k}f{q}_{i}E\left({q}_{i},M\right)\right)$ 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 ${\sum }_{c\in Mc}|c|\le S$ coral reefs optimization algorithm (CROMVS) 8 MVPP, K = Number of generating populations, M = Number of Queries, N = Number of Relations, H = threshold times, Fa = Fraction of asexual reproduction, Fb = Ratio of number of selected solutions, Fd = Fraction of the worst solutions $\begin{array}{l}{f}_{x}={\sum }_{i\in M}\left({\sum }_{q\in Q}e{f}_{q}\ast {C}_{i}^{q}\right)\\ -\left({\sum }_{u\in Prej\cap x}{\sum }_{q\in Q}e{f}_{q}\ast {C}_{u}^{q}\\ +{\sum }_{r\in R}u{f}_{r}\ast {C}_{i}^{r}\right)\end{array}$ MV with MAX(fx) 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(fx) Multi- Objective MONPGA. 5 L: Size of each view, Pc: probability of crossover, Pm: 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 ufi: update frequency for Ri. $Q=\left\{{Q}_{1},{Q}_{2},\cdots ,{Q}_{q}\right\}$ : Set of queries, efi execution frequency for Qi. $\begin{array}{l}{g}_{x}={\sum }_{i\in M}\left({\sum }_{r\in R}u{f}_{r}\ast {C}_{i}^{r}\\ +{\sum }_{q\in Q}e{f}_{q}\ast {C}_{i}^{q}\right)\end{array}$ 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.  M: list of nodes in MVPP-Player 1 union Player 2. materialized view List Map-Reduce model (MR-MVPP) 7 Q: workload of queries fq: list of query frequencies R: base relations fu: list of update frequencies b: number of categories A: a number between 0 and 1 for hash function t: threshold of similarity $Q{C}_{i}={f}_{qi}\ast {\sum }_{\left\{j|{Q}_{i}\in Query\left({V}_{j}\right)\right\}}A\text{ }Cost\left({V}_{j}\right)$ 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. $Jaccard\left(A,B\right)=\frac{|A|\cap |B|}{|A|\cup |B|}$ MVPP with least total cost = Min(QCi)