PHF Algorithms and Minimality

Lecture 16 details the algorithmic formulation of complete and minimal simple predicate sets for Primary Horizontal Fragmentation. A set of simple predicates Pr is complete if and only if there is an equal probability of access by every application to any tuple belonging to any minterm fragment. The set Pr is minimal if all its predicates are relevant in determining the fragmentation. Students study the formal COM_MIN algorithm, which iteratively evaluates candidate predicates against existing minterm fragments, selecting only those predicates that actively partition an existing fragment into sub-fragments with distinct application access probabilities. The lecture covers the elimination of contradictory or unsatisfiable minterms (e.g., Salary > 50000 AND Salary < 30000) using semantic integrity constraints, ensuring the final fragment set is parsimonious, minimal, and computationally efficient. Students investigate the role of global data dictionaries and catalog managers in resolving location-independent queries across networked nodes. The discussion highlights how horizontal and vertical data fragmentation techniques reduce disk I/O, minimize message traffic, and maximize localized query execution. Key concepts such as minterm predicate generation, completeness conditions, and disjointness rules are rigorously analyzed in empirical design scenarios. The lecture details derived horizontal fragmentation mechanisms, utilizing owner-member relationships and foreign key dependencies to optimize join operations. Vertical fragmentation methodologies are demonstrated using attribute affinity matrices and the Bond Energy Algorithm to cluster frequently accessed columns. Data replication architectures, including snapshot, transactional, and merge replication models, are evaluated for operational availability and consistency. Formal transaction management frameworks analyze ACID properties in distributed environments, ensuring database integrity despite concurrent site failures. 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.