ecommendation algebra that is used for defining certain" core"parts of REQUEST queries. We also describe how these core reQueST queries can be processed by mapping them into this algebra This paper makes the following contributions. It proposes language REQUEST for expressing flexible user-driven recommendations and presents its syntax and semantics. It also presents recommendation algebra RA, which enhances the systematic definition of REQUEST. We also show how the core rEQUeSt queries can be mapped into RA, thus providing a way to process these queries and compare the expressive power of REQUESt and ra 2. Background: Multidimensional Recommender Systems A multidimensional ratings cube is defined as a tuple(D, M, H, E, L)as follows Dimensions D). D=id,, d,2,. dni is a set of n dimensions, where each d, is a dimension name. For example, in addition to the standard User and Movie dimensions of the traditional movie recommender systems, such as Movielens [19], we consider other contextual dimensions [4, 5], such as Time, Theater and Companion, i.e., D=(User, Movie, Time, Theater, Companion) Attribute Hierarchies(H). Each dimension d; is represented by a set of attributes AF(ai, ., ait) where each ai is an attribute name; e.g. Atime=(Date, DayOfWeek, TimeOfWeek, Month, Quarter, Year). The domain of attribute x of dimension d is denoted as dom(dx), e.g., dom(Time. DayOfWeek)= Mon, Tue, Wed, Thu, Fri, Sat, Sun) and dom(Time. TimeOfWeek)= weekday, weekend j The multidimensional recommendation model allows for OLAP-based aggregation hierarchies [4, 5 that help aggregate ratings according to the methods described in [4]. In particular, attributes A, of dimension d; form a directed acyclic graph(i.e, a hierarchy )H;=(Ai, Ei) with set of nodes A; (i.e, each ode corresponds to an attribute)and set of edges Ei. There exists a directed edge in Hi from attribute E Ai to attribute y e Ai, iff every value of x uniquely determines the value of y, i.e., if attribute y is functionally dependent on attribute x. Such an edge will be denoted (x, y)or x]y. We will assume that has a single root node, Root(Hi, which we will call the key dimension attribute, consistent with the standard database terminology. Let H=( H1,..., Hn) Given hierarchy H, and attribute di- x EAi, we define SubGraph(H, d; x)to be a subgraph of H; rooted6 recommendation algebra that is used for defining certain “core” parts of REQUEST queries. We also describe how these core REQUEST queries can be processed by mapping them into this algebra. This paper makes the following contributions. It proposes language REQUEST for expressing flexible user-driven recommendations and presents its syntax and semantics. It also presents recommendation algebra RA, which enhances the systematic definition of REQUEST. We also show how the core REQUEST queries can be mapped into RA, thus providing a way to process these queries, and compare the expressive power of REQUEST and RA. 2. Background: Multidimensional Recommender Systems A multidimensional ratings cube is defined as a tuple (D, M, H, E, L) as follows. Dimensions (D). D = {d1, d2, …, dn} is a set of n dimensions, where each di is a dimension name. For example, in addition to the standard User and Movie dimensions of the traditional movie recommender systems, such as MovieLens [19], we consider other contextual dimensions [4, 5], such as Time, Theater and Companion., i.e., D = {User, Movie, Time, Theater, Companion}. Attribute Hierarchies (H). Each dimension di is represented by a set of attributes Ai={ai1, …, ait} where each aij is an attribute name; e.g. Atime={Date, DayOfWeek, TimeOfWeek, Month, Quarter, Year}. The domain of attribute x of dimension d is denoted as dom(d.x), e.g., dom(Time.DayOfWeek) = { Mon, Tue, Wed, Thu, Fri, Sat, Sun } and dom(Time.TimeOfWeek) = { weekday, weekend }. The multidimensional recommendation model allows for OLAP-based aggregation hierarchies [4, 5] that help aggregate ratings according to the methods described in [4]. In particular, attributes Ai of dimension di form a directed acyclic graph (i.e., a hierarchy) Hi = (Ai, Ei) with set of nodes Ai (i.e., each node corresponds to an attribute) and set of edges Ei. There exists a directed edge in Hi from attribute x ∈ Ai to attribute y ∈ Ai, iff every value of x uniquely determines the value of y, i.e., if attribute y is functionally dependent on attribute x. Such an edge will be denoted (x, y) or xÆy. We will assume that Hi has a single root node, Root(Hi), which we will call the key dimension attribute, consistent with the standard database terminology. Let H = { H1, …, Hn }. Given hierarchy Hi and attribute di.x ∈Ai, we define SubGraph(Hi, di.x) to be a subgraph of Hi rooted