Graph Composition Framework for Web Services

• Graph Composition Framework is a graph-theoretic approach that models web services as vertices in a directed weighted graph, integrating semantic matching with non-functional criteria.
• It employs an extended Floyd–Warshall algorithm to precompute all-pairs shortest paths, drastically reducing online computation and improving service discovery.
• The framework ensures global optimality, scalability, and rapid response in e-government systems through dynamic update handling and optimized predecessor matrices.

The graph composition framework, as described in the context of e-government web service composition, is a graph-theoretic approach for modeling and optimizing the automated composition of web services. By representing web services and their semantic relationships as a directed weighted graph, the framework enables efficient discovery and execution of composite services that satisfy complex user requirements through the computation of optimal execution paths. The framework notably employs an extended version of the Floyd–Warshall algorithm to precompute shortest paths, minimizing online computation and offering substantial improvements in efficiency, scalability, and quality of service for public administration systems.

1. Graph-Theoretic Modeling of Service Composition

The core of the framework is the Service Composition Graph (SCG), a directed weighted graph $G = (V, E, W)$, where:

• $V$ is the set of vertices, each representing a specific web service.
• $E$ is the set of directed edges, where an edge from $V_i$ to $V_j$ exists if the output of service $V_i$ can semantically match (or be subsumed by) the input of service $V_j$.
• $W$ is the set of weights on edges, computed as a sum of semantic similarity measures and non-functional property values (such as cost, execution time, and availability):

$W_{ij} = f(QOS(V_i)) + S_{ij}$

where $S_{ij}$ quantifies the semantic similarity between services and $f(QOS(V_i))$ aggregates relevant non-functional properties.

This formalization allows the SCG to encode the feasible interactions among all available web services, taking into account both their functionalities (semantics) and operational characteristics.

2. Semantic Relationship and Edge Weight Calculation

Semantic matching in the SCG is performed through subsumption-based reasoning on service parameters (using ontological descriptions such as OWL-S). For a pair $(V_i, V_j)$, an edge is created only if the semantic relationship between $V_i$’s outputs and $V_j$’s inputs falls into one of these categories:

• Exact match: Concepts are logically equivalent.
• Plug-in match: Output is a sub-concept of the input (target subsumes source).
• Subsumes match: Input is a sub-concept of the output (source subsumes target).
• Fail match: No semantic relationship found (no edge).

The weight calculation incorporates these semantic distinctions alongside non-functional criteria. This encoding ensures that the graph structure reflects both the feasibility and desirability (in terms of quality attributes) of chaining services.

3. Extended Floyd–Warshall Algorithm for Path Computation

The primary algorithmic innovation is the use of an extended Floyd–Warshall algorithm to compute all-pairs shortest paths in $G$ and to reconstruct the actual service sequences (paths) needed for composition:

• Offline Precomputation: During service publication or update, the extended algorithm computes the shortest weighted paths between all service pairs, storing both the minimal costs (in a DIST matrix) and the corresponding paths (in a NEXT or predecessor matrix).
• Path Reconstruction: Unlike the classic Floyd–Warshall, this version retains enough auxiliary information to reconstruct the full ordered list of services composing the optimal path between any two nodes.
• Online Composition: Given a user query, the system retrieves the appropriate precomputed path, avoiding expensive real-time graph traversal or search.

This precomputation strategy shifts the dominant computational cost to the offline phase, which is advantageous when frequent queries are expected over a relatively stable service catalog.

4. Optimization Techniques

Key optimizations include:

• Shortest Predecessor Matrix (SPM): All shortest paths are stored for rapid lookup, ensuring near-instantaneous extraction of optimal compositions for incoming requests.
• Dynamic Update Handling: When services are added, updated, or removed, only the affected portions of the SCG and SPM need to be updated, thus localizing the computational impact.
• Minimization of Online Overhead: By making the heavy computation offline, runtime costs (in response latency and computational resources) are significantly lowered.

This design inherently supports scaling to large numbers of services, provided the SCG updates are managed efficiently.

5. Practical Implications and Deployment Considerations

The framework has direct implications for e-government systems:

• Efficiency: Dramatic reductions in end-to-end service composition time, as user requests are resolved by reading from the SPM rather than dynamic graph search.
• Quality of Service: By integrating both functional matches and operational attributes, the optimal selection balances correctness and resource efficiency.
• Flexibility and Adaptivity: The architecture accommodates dynamic service environments, recalculating only when necessary.
• User Transparency: The complexity of composite service resolution is entirely abstracted from the end-user, contributing to a seamless experience.

By precomputing all feasible compositions, administrative systems can effectively guarantee both rapid execution and policy-compliant quality levels.

6. Comparative Analysis

Relative to alternative web service composition methods, the SCG with extended Floyd–Warshall precomputation displays several comparative advantages:

• Precomputation versus On-the-fly Search: Unlike runtime approaches such as A*, Dijkstra’s algorithm, or chaining methods, which build and traverse dependency graphs on demand, this framework achieves substantial speedups by storing all relevant paths ahead of time.
• Global Optimality: The use of the all-pairs shortest path guarantees that the selected composition is globally optimal (minimum cumulative cost or highest composite preference).
• Simplicity and Maintainability: The approach simplifies integration and maintenance, critical in environments where public services and interfaces are subject to change and regulatory oversight.
• Scalability: Shifting computation to the publication phase enables scalable handling of large-scale service ecosystems, assuming incremental updates are efficiently managed.

7. Extension Beyond E-Government and Future Directions

Although tailored for e-government service composition, the SCG framework’s principles—semantic graph modeling, weighted edge definitions, and offline global path computation—are directly transferable to broader service-oriented architectures, composite workflow planning, or any domain where optimal chaining of modular operations is required. Enhancement of semantic matchmaking algorithms, dynamic graph update mechanisms, and integration with distributed, federated service registries represent promising directions for future development and application.