Data Localization for Horizontal & Vertical Fragments

Lecture 39 addresses Data Localization, the second phase of distributed query processing. Data localization maps the canonical global algebraic query tree into a localized query tree defined over physical fragments. In the generic localization program, every global relation is substituted by its reconstruction formula (unions for horizontal fragments, natural joins for vertical fragments). Because this initial substitution generates redundant union and join operations, reduction algorithms are applied. The lecture details reduction for primary horizontal fragmentation: pushing selection predicates into union branches and eliminating fragments whose qualification predicates contradict the query predicate. Reduction for vertical fragmentation prunes fragments whose attribute sets contain none of the projected or queried attributes (except primary keys), substantially trimming execution trees. Serializability theory and conflict equivalence criteria provide mathematical foundations for proving the correctness of interleaved transaction schedules. Locking-based concurrency control protocols, including Two-Phase Locking, Distributed 2PL, and primary copy 2PL, are scrutinized for lock contention trade-offs. Distributed deadlock detection and resolution algorithms examine wait-for graphs, probe messages, and priority-based prevention strategies. Timestamp-ordering concurrency control mechanisms illustrate how physical and logical timestamps enforce serial ordering without deadlock vulnerability. Multi-version and conservative timestamp ordering algorithms are analyzed for read-heavy workloads and long-duration distributed transactions. Distributed query processing lifecycles trace query decomposition, algebraic normalization, semantic analysis, and elimination of redundant operations. Data localization algorithms transform global algebraic operator trees into localized fragment queries using relational reduction rules. Heuristic query optimization techniques illustrate how selection and projection operations are pushed down close to local physical fragments. Cost-based query optimization models analyze CPU overhead, disk page access costs, and communication network transmission delays. Distributed join optimization strategies contrast broadcast joins, partitioned hash joins, and semi-join reducers like the SDD-1 algorithm. Distributed reliability architectures examine failure classifications, including transaction aborts, site crashes, and network partitioning anomalies. Atomic commitment protocols, notably Two-Phase Commit (2PC) and Three-Phase Commit (3PC), are demonstrated with formal state transition diagrams. Parallel database system architectures, spanning Shared-Memory, Shared-Disk, and Shared-Nothing topologies, are contrasted for speedup and scaleup performance.