Testing for Conflict Serializability of a Schedule
21.5.2 Testing for Conflict Serializability of a Schedule
There is a simple algorithm for determining whether a particular schedule is con- flict serializable or not. Most concurrency control methods do not actually test for serializability. Rather protocols, or rules, are developed that guarantee that any schedule that follows these rules will be serializable. We discuss the algorithm for testing conflict serializability of schedules here to gain a better understanding of these concurrency control protocols, which are discussed in Chapter 22.
Algorithm 21.1 can be used to test a schedule for conflict serializability. The algo- rithm looks at only the read_item and write_item operations in a schedule to construct
a precedence graph (or serialization graph), which is a directed graph G = (N, E) that consists of a set of nodes N = {T 1 ,T 2 , ..., T n } and a set of directed edges E = {e 1 ,
e 2 , ..., e m }. There is one node in the graph for each transaction T i in the schedule. Each edge e i in the graph is of the form (T j →T k ), 1 ≤ j ≤ n, 1 ≤ k f n, where T j is the starting node of e i and T k is the ending node of e i . Such an edge from node T j to
12 We will use serializable to mean conflict serializable. Another definition of serializable used in practice
764 Chapter 21 Introduction to Transaction Processing Concepts and Theory
node T k is created by the algorithm if one of the operations in T j appears in the schedule before some conflicting operation in T k .
Algorithm 21.1. Testing Conflict Serializability of a Schedule S
1. For each transaction T i participating in schedule S, create a node labeled T i in the precedence graph.
2. For each case in S where T j executes a read_item (X) after T i executes a write_item (X), create an edge (T i →T j ) in the precedence graph.
3. For each case in S where T j executes a write_item (X) after T i executes a read_item (X), create an edge (T i →T j ) in the precedence graph.
4. For each case in S where T j executes a write_item (X) after T i executes a write_item (X), create an edge (T i →T j ) in the precedence graph.
5. The schedule S is serializable if and only if the precedence graph has no cycles.
The precedence graph is constructed as described in Algorithm 21.1. If there is a cycle in the precedence graph, schedule S is not (conflict) serializable; if there is no cycle, S is serializable. A cycle in a directed graph is a sequence of edges C = ((T j → T k ), (T k →T p ), ..., (T i →T j )) with the property that the starting node of each edge—except the first edge—is the same as the ending node of the previous edge, and the starting node of the first edge is the same as the ending node of the last edge (the sequence starts and ends at the same node).
In the precedence graph, an edge from T i to T j means that transaction T i must come before transaction T j in any serial schedule that is equivalent to S, because two con- flicting operations appear in the schedule in that order. If there is no cycle in the
to S, by ordering the transactions that participate in S as follows: Whenever an edge exists in the precedence graph from T
to T j ,T i must appear before T j in the equiva- Notice that the edges (T i →T j ) in a precedence graph can optionally be labeled by the name(s) of the data item(s) that led to creating the edge. Figure 21.7 shows such labels on the edges.
13 i
In general, several serial schedules can be equivalent to S if the precedence graph for S has no cycle. However, if the precedence graph has a cycle, it is easy to show that we cannot create any equivalent serial schedule, so S is not serializable. The prece- dence graphs created for schedules A to D, respectively, in Figure 21.5 appear in Figure 21.7(a) to (d). The graph for schedule C has a cycle, so it is not serializable. The graph for schedule D has no cycle, so it is serializable, and the equivalent serial
schedule is T 1 followed by T 2 . The graphs for schedules A and B have no cycles, as
expected, because the schedules are serial and hence serializable. Another example, in which three transactions participate, is shown in Figure 21.8.
Figure 21.8(a) shows the read_item and write_item operations in each transaction. Two schedules E and F for these transactions are shown in Figure 21.8(b) and (c),
21.5 Characterizing Schedules Based on Serializability 765
Constructing the precedence graphs for schedules A to D from Figure 21.5 to test for conflict serializability. (a) Precedence graph for serial schedule A. (b) Precedence graph for serial schedule B. (c) Precedence graph for schedule C (not serializable). (d) Precedence graph for schedule D (serializable, equivalent to schedule A).
respectively, and the precedence graphs for schedules E and F are shown in parts (d) and (e). Schedule E is not serializable because the corresponding precedence graph has cycles. Schedule F is serializable, and the serial schedule equivalent to F is shown in Figure 21.8(e). Although only one equivalent serial schedule exists for F, in gen- eral there may be more than one equivalent serial schedule for a serializable sched- ule. Figure 21.8(f) shows a precedence graph representing a schedule that has two equivalent serial schedules. To find an equivalent serial schedule, start with a node that does not have any incoming edges, and then make sure that the node order for every edge is not violated.
Parts
» Fundamentals_of_Database_Systems,_6th_Edition
» Characteristics of the Database Approach
» Advantages of Using the DBMS Approach
» A Brief History of Database Applications
» Schemas, Instances, and Database State
» The Three-Schema Architecture
» The Database System Environment
» Centralized and Client/Server Architectures for DBMSs
» Classification of Database Management Systems
» Domains, Attributes, Tuples, and Relations
» Key Constraints and Constraints on NULL Values
» Relational Databases and Relational Database Schemas
» Integrity, Referential Integrity, and Foreign Keys
» Update Operations, Transactions, and Dealing with Constraint Violations
» SQL Data Definition and Data Types
» Specifying Constraints in SQL
» The SELECT-FROM-WHERE Structure of Basic SQL Queries
» Ambiguous Attribute Names, Aliasing, Renaming, and Tuple Variables
» Substring Pattern Matching and Arithmetic Operators
» INSERT, DELETE, and UPDATE Statements in SQL
» Comparisons Involving NULL and Three-Valued Logic
» Nested Queries, Tuples, and Set/Multiset Comparisons
» The EXISTS and UNIQUE Functions in SQL
» Joined Tables in SQL and Outer Joins
» Grouping: The GROUP BY and HAVING Clauses
» Discussion and Summary of SQL Queries
» Specifying General Constraints as Assertions in SQL
» Introduction to Triggers in SQL
» Specification of Views in SQL
» View Implementation, View Update, and Inline Views
» Schema Change Statements in SQL
» Sequences of Operations and the RENAME Operation
» The UNION, INTERSECTION, and MINUS Operations
» The CARTESIAN PRODUCT (CROSS PRODUCT) Operation
» Variations of JOIN: The EQUIJOIN and NATURAL JOIN
» Additional Relational Operations
» Examples of Queries in Relational Algebra
» The Tuple Relational Calculus
» The Domain Relational Calculus
» Using High-Level Conceptual Data Models
» Entity Types, Entity Sets, Keys, and Value Sets
» Relationship Types, Relationship Sets, Roles, and Structural Constraints
» ER Diagrams, Naming Conventions, and Design Issues
» Example of Other Notation: UML Class Diagrams
» Relationship Types of Degree Higher than Two
» Subclasses, Superclasses, and Inheritance
» Constraints on Specialization and Generalization
» Specialization and Generalization Hierarchies
» Modeling of UNION Types Using Categories
» A Sample UNIVERSITY EER Schema, Design Choices, and Formal Definitions
» Data Abstraction, Knowledge Representation, and Ontology Concepts
» ER-to-Relational Mapping Algorithm
» Discussion and Summary of Mapping for ER Model Constructs
» Mapping EER Model Constructs
» The Role of Information Systems
» The Database Design and Implementation Process
» Use of UML Diagrams as an Aid to Database Design Specification 6
» Rational Rose: A UML-Based Design Tool
» Automated Database Design Tools
» Introduction to Object-Oriented Concepts and Features
» Object Identity, and Objects versus Literals
» Complex Type Structures for Objects and Literals
» Encapsulation of Operations and Persistence of Objects
» Type Hierarchies and Inheritance
» Other Object-Oriented Concepts
» Object-Relational Features: Object Database Extensions to SQL
» Overview of the Object Model of ODMG
» Built-in Interfaces and Classes in the Object Model
» Atomic (User-Defined) Objects
» Extents, Keys, and Factory Objects
» The Object Definition Language ODL
» Differences between Conceptual Design of ODB and RDB
» Mapping an EER Schema to an ODB Schema
» Query Results and Path Expressions
» Overview of the C++ Language Binding in the ODMG Standard
» Structured, Semistructured, and Unstructured Data
» XML Hierarchical (Tree) Data Model
» Well-Formed and Valid XML Documents and XML DTD
» XPath: Specifying Path Expressions in XML
» XQuery: Specifying Queries in XML
» Extracting XML Documents from
» Database Programming: Techniques
» Retrieving Single Tuples with Embedded SQL
» Retrieving Multiple Tuples with Embedded SQL Using Cursors
» Specifying Queries at Runtime Using Dynamic SQL
» SQLJ: Embedding SQL Commands in Java
» Retrieving Multiple Tuples in SQLJ Using Iterators
» Database Programming with SQL/CLI Using C
» JDBC: SQL Function Calls for Java Programming
» Database Stored Procedures and SQL/PSM
» PHP Variables, Data Types, and Programming Constructs
» Overview of PHP Database Programming
» Imparting Clear Semantics to Attributes in Relations
» Redundant Information in Tuples and Update Anomalies
» Normal Forms Based on Primary Keys
» General Definitions of Second and Third Normal Forms
» Multivalued Dependency and Fourth Normal Form
» Join Dependencies and Fifth Normal Form
» Inference Rules for Functional Dependencies
» Minimal Sets of Functional Dependencies
» Properties of Relational Decompositions
» Dependency-Preserving Decomposition
» Dependency-Preserving and Nonadditive (Lossless) Join Decomposition into 3NF Schemas
» Problems with NULL Values and Dangling Tuples
» Discussion of Normalization Algorithms and Alternative Relational Designs
» Further Discussion of Multivalued Dependencies and 4NF
» Other Dependencies and Normal Forms
» Memory Hierarchies and Storage Devices
» Hardware Description of Disk Devices
» Magnetic Tape Storage Devices
» Placing File Records on Disk
» Files of Unordered Records (Heap Files)
» Files of Ordered Records (Sorted Files)
» External Hashing for Disk Files
» Hashing Techniques That Allow Dynamic File Expansion
» Other Primary File Organizations
» Parallelizing Disk Access Using RAID Technology
» Types of Single-Level Ordered Indexes
» Some General Issues Concerning Indexing
» Algorithms for External Sorting
» Implementing the SELECT Operation
» Implementing the JOIN Operation
» Algorithms for PROJECT and Set
» Notation for Query Trees and Query Graphs
» Heuristic Optimization of Query Trees
» Catalog Information Used in Cost Functions
» Examples of Cost Functions for SELECT
» Examples of Cost Functions for JOIN
» Example to Illustrate Cost-Based Query Optimization
» Factors That Influence Physical Database Design
» Physical Database Design Decisions
» An Overview of Database Tuning in Relational Systems
» Transactions, Database Items, Read and Write Operations, and DBMS Buffers
» Why Concurrency Control Is Needed
» Transaction and System Concepts
» Desirable Properties of Transactions
» Serial, Nonserial, and Conflict-Serializable Schedules
» Testing for Conflict Serializability of a Schedule
» How Serializability Is Used for Concurrency Control
» View Equivalence and View Serializability
» Types of Locks and System Lock Tables
» Guaranteeing Serializability by Two-Phase Locking
» Dealing with Deadlock and Starvation
» Concurrency Control Based on Timestamp Ordering
» Multiversion Concurrency Control Techniques
» Validation (Optimistic) Concurrency
» Granularity of Data Items and Multiple Granularity Locking
» Using Locks for Concurrency Control in Indexes
» Other Concurrency Control Issues
» Recovery Outline and Categorization of Recovery Algorithms
» Caching (Buffering) of Disk Blocks
» Write-Ahead Logging, Steal/No-Steal, and Force/No-Force
» Transaction Rollback and Cascading Rollback
» NO-UNDO/REDO Recovery Based on Deferred Update
» Recovery Techniques Based on Immediate Update
» The ARIES Recovery Algorithm
» Recovery in Multidatabase Systems
» Introduction to Database Security Issues 1
» Discretionary Access Control Based on Granting and Revoking Privileges
» Mandatory Access Control and Role-Based Access Control for Multilevel Security
» Introduction to Statistical Database Security
» Introduction to Flow Control
» Encryption and Public Key Infrastructures
» Challenges of Database Security
» Distributed Database Concepts 1
» Types of Distributed Database Systems
» Distributed Database Architectures
» Data Replication and Allocation
» Example of Fragmentation, Allocation, and Replication
» Query Processing and Optimization in Distributed Databases
» Overview of Transaction Management in Distributed Databases
» Overview of Concurrency Control and Recovery in Distributed Databases
» Current Trends in Distributed Databases
» Distributed Databases in Oracle 13
» Generalized Model for Active Databases and Oracle Triggers
» Design and Implementation Issues for Active Databases
» Examples of Statement-Level Active Rules
» Time Representation, Calendars, and Time Dimensions
» Incorporating Time in Relational Databases Using Tuple Versioning
» Incorporating Time in Object-Oriented Databases Using Attribute Versioning
» Temporal Querying Constructs and the TSQL2 Language
» Spatial Database Concepts 24
» Multimedia Database Concepts
» Clausal Form and Horn Clauses
» Datalog Programs and Their Safety
» Evaluation of Nonrecursive Datalog Queries
» Introduction to Information Retrieval
» Types of Queries in IR Systems
» Evaluation Measures of Search Relevance
» Web Analysis and Its Relationship to Information Retrieval
» Analyzing the Link Structure of Web Pages
» Approaches to Web Content Analysis
» Trends in Information Retrieval
» Data Mining as a Part of the Knowledge
» Goals of Data Mining and Knowledge Discovery
» Types of Knowledge Discovered during Data Mining
» Market-Basket Model, Support, and Confidence
» Frequent-Pattern (FP) Tree and FP-Growth Algorithm
» Other Types of Association Rules
» Approaches to Other Data Mining Problems
» Commercial Data Mining Tools
» Data Modeling for Data Warehouses
» Difficulties of Implementing Data Warehouses
» Grouping, Aggregation, and Database Modification in QBE
Show more