Shareability-Network Framework Overview

Updated 27 December 2025

The shareability-network framework is a formalism for modeling, quantifying, and optimizing resource or information sharing by representing pairwise or multilateral compatibility as a network.
It constructs shareability graphs and employs algorithms like maximum matching, network flows, and set partitioning to efficiently solve combinatorial sharing problems.
Its applications span urban transportation, quantum networks, and IoT resource allocation, delivering measurable gains in efficiency and scalability.

The shareability-network framework is a formalism for modeling, quantifying, and optimizing the potential for resource or information sharing among agents, requests, or items, by representing pairwise or multilateral compatibility as a network. In this framework, nodes represent requests, users, trips, or data objects, and edges indicate the feasibility or attractiveness of sharing under application-specific constraints, such as spatiotemporal, value, or policy criteria. The framework arose independently in domains including urban transportation, quantum networks, social media diffusion, wireless resource allocation, and open data evaluation, where it enables tractable optimization and yields structural and predictive insights unattainable via non-networked approaches.

1. Core Definitions and Graph Structures

The fundamental object in the shareability-network framework is the shareability graph, which encodes the feasible pairing (and, in general, grouping) of requests or agents.

Unipartite Shareability Graph: Nodes correspond to ride requests, trips, or agents. An edge links two nodes if the corresponding pair can feasibly share a resource (e.g., ride, bus, spectrum, information), complying with constraints such as maximum delay, deadline, reliability, or detour (Santi et al., 2013, Librino et al., 28 Feb 2025, Zhan et al., 2024, Guo et al., 2020, JS et al., 2021).
Bipartite Representation: Some variants introduce explicit ride, group, or trip nodes (bipartite graph), allowing for modeling of multi-party pooling and facilitating assignment formulations (Bujak et al., 2022).
Weighted Aggregates: In probabilistic or dynamic contexts, the shareability graph can be weighted by the frequency or utility of each edge/group being feasible under stochastic parameters or across replications (Bujak et al., 2022).

Formally, for transportation pooling, a shareability network $G=(V,E)$ is defined with:

$V=$ set of requests/trips,
$E= \{(i,j) : \text{requests } i \text{ and } j \text{ are mutually shareable under given constraints}\}$ .

In quantum networks, the shareability network is typically a directed graph where an edge from node $A$ to $B$ indicates a quantum correlation or steering relation (Hao et al., 2021, Song et al., 2024).

2. Mathematical Formulation and Algorithmic Construction

Shareability-network-based optimization typically proceeds in two stages: (i) construction of the network, (ii) solution of a combinatorial selection or assignment problem over the network.

Graph Construction:

Feasibility Evaluation: For each candidate pair or group, enumerate possible sequences, check if all constraints (e.g., maximum additional travel time, joint reliability in URLLC, measurement settings) are satisfied (Santi et al., 2013, Librino et al., 28 Feb 2025, Zhan et al., 2024, Hao et al., 2021).
Edge Pruning and Node Compression: Large-scale practical systems often require reducing density via spatial or temporal indexing, clustering (e.g., bus stop aggregation), or quasi-clique approximations (Guo et al., 2020, Zhan et al., 2024).
Probabilistic/Utility Weights: In behavioral or stochastic settings, edges are sampled or weighted according to utility models or observed sharing rates (Bujak et al., 2022).

Optimization Problems:

Maximum Matching: Selecting a maximal set of disjoint shareable groups, often to maximize the number of shared trips or pooled requests (Santi et al., 2013, Zhan et al., 2024, Librino et al., 28 Feb 2025).
Weighted Assignment/Set Partitioning: Incorporating trip cost, savings, spectral efficiency, or penalties for unserved requests, sometimes via integer linear programs or network flows (Guo et al., 2020, Librino et al., 28 Feb 2025).
Network Flow Formulations: In online dispatch or dataset sharing, modeling driver–order or data–reuse assignment as flows through an extended shareability network, sometimes augmented with opportunity-aware weights such as sink proximity (Wang et al., 20 Dec 2025, Sudheendra et al., 17 Nov 2025).

Implementation scales polynomially in problem size due to the reduction from combinatorial search over all groupings to tractable graph-theoretic problems (e.g., matching, flow), particularly when sparse or pruned (Santi et al., 2013, Bujak et al., 2022).

3. Application Domains and Metrics

Transportation and Mobility

Ride-Pooling: Nodes are trip requests; edges exist for pairs (or, in clique algorithms, groups) that can be jointly served without violating user delay tolerances. Solutions via maximum matching yield system-level reductions in vehicle miles traveled (VMT), cost, and emissions, with empirical findings of up to 30–40% VMT reduction and rapid saturation of shareability with trip density (Santi et al., 2013, Tachet et al., 2016).
Routing (School Buses): Shareability substructures (cliques) facilitate decomposition of the classical VRP into assignment over feasible pooled trips, resulting in dramatically smaller integer program size and practical scalability (Guo et al., 2020).
Resource Allocation (IoT/URLLC): Devices can share RUs (resource units) if their transmission windows and reliability budgets overlap. Matching on the shareability graph sharpens spectral efficiency by 50% over orthogonal allocation, with maintained fairness metrics (Librino et al., 28 Feb 2025).
Network-Level Shareability Metrics: The maximum network flow overlap problem (MNFLOP) generalizes trip overlap (average number of co-traversals per link) and supports fine-grained and aggregate metrics of shareability and demand dispersion (JS et al., 2021).

Quantum Networks

Steering and Correlation Shareability: Directed shareability networks represent the set of parties that can steer or correlate with others under given resources and measurement settings, underpinning monogamy and shareability inequalities; the graphical structure encodes the distribution and limitation of quantum resources (Mukherjee et al., 2017, Hao et al., 2021, Song et al., 2024).

Social Media/Content Sharing: Shareability is modeled as an edge-weighted network factoring in sender preference, recipient preference, and item salience, leading to improved prediction of sharing cascades and refinement of diffusion models (Sharma et al., 2014, Gleeson et al., 2015).
Open-Data Impact Metrics: The X-index aggregates dataset-level value scores across a data-shareability network, incorporating breadth of reuse, FAIRness, cross-disciplinary diversity, and transitive reuse depth (via weighted citation networks) (Sudheendra et al., 17 Nov 2025).

4. Network Analysis, Structural Properties, and Predictive Use

Comprehensive network analysis of shareability structures reveals:

Clique Density and Fragmentation: Simple shareability graphs (potential sharing) are typically dense with giant components, but feasible matchings/matchings are sparse and highly fragmented, reflecting combinatorial constraints (Bujak et al., 2022).
Weighted Edge Distributions: Repeated stochastic or utility-based assignment yields edge weights clustered near either zero or the total number of replicates, identifying “sure” and “noisy” sharing opportunities (Bujak et al., 2022).
Topological Diagnostics: Degree distribution, clustering coefficient, betweenness centrality, and giant-component size inform both system-level policy (e.g., targeted incentives, fleet sizing) and the structure of epidemic risk or information propagation (Bujak et al., 2022, JS et al., 2021).
Empirical Saturation and Universality: In urban pooling, shareability as a function of the rescaled trip density collapses to a universal curve across cities, revealing fundamental limits of efficiency irrespective of local heterogeneity (Tachet et al., 2016).

5. Algorithmic Strategies and Complexity

The shareability-network framework enables scalable solution methods:

Matching Algorithms: Edmonds’ blossom for maximum matching, Hungarian for bipartite assignment, and heuristic hierarchical clique enumeration for multi-sharing (Santi et al., 2013, Zhan et al., 2024).
Decomposition and Compression: Node aggregation and edge pruning to manage computational resources without sacrificing optimality for large-scale applications (Guo et al., 2020).
Online Model-Predictive Control: Receding-horizon models for real-time dispatching can enrich edge weights with opportunity or “sink proximity” to bias toward orders unlocking future capacity, with observed gains in request-service rate (Wang et al., 20 Dec 2025).
Probabilistic Reweighted Graphs: Compiling numerous stochastic replicates to extract robust or marginal shareability links under behavioral uncertainty (Bujak et al., 2022).
Set Partitioning/Assignment: Exploitation of shareable-trip enumeration to reduce complex scheduling/routing problems to assignment over feasible trip pools (Santi et al., 2013, Guo et al., 2020, Librino et al., 28 Feb 2025).

Algorithmic complexity is generally polynomial in the size of the input, provided careful edge and group pruning (Santi et al., 2013, Guo et al., 2020, Zhan et al., 2024).

6. Limitations and Applicability Conditions

Explicit limitations of the shareability-network framework depend on domain:

Transportation Models: Assumptions include homogeneous average speed, idealized route geometry, uniform demand distribution, and primarily pairwise (k=2) sharing. Complexity rises sharply for k>2 multi-party pooling as hypergraph matching becomes NP-hard (Santi et al., 2013, Tachet et al., 2016).
Social and Information Diffusion: Behavioral preference estimation and dynamic salience operationalization may be domain- or UI-specific; cross-domain generalization requires care (Sharma et al., 2014, Gleeson et al., 2015).
Quantum Shareability: Directionality, measurement setting choices, and system dimension (qubits vs qudits) constrain the applicability of network-level monogamy and shareability theorems (Mukherjee et al., 2017, Hao et al., 2021, Song et al., 2024).
Data Impact Metrics: Citation networks for transitive reuse are as robust as the linked data and field-labeling systems allow; transitive weights and breadth proxies may require domain expertise for tuning (Sudheendra et al., 17 Nov 2025).

The framework is most effective for applications where pairwise/group compatibility is tractable to compute and where network structure admits meaningful sparsification.

7. Broader Implications and Cross-Domain Extensions

The shareability-network framework provides a unifying structural approach across transportation, quantum information, wireless communications, and data science. Its applications include:

Policy design for shared mobility and fleet operations, with empirically validated recommendations for delay tolerances, matching policy, and system size (Santi et al., 2013, Tachet et al., 2016);
Quantum resource allocation, protocol design for distributed cryptography, and detection of genuinely multipartite entangled states (Mukherjee et al., 2017, Hao et al., 2021, Song et al., 2024);
Design and evaluation of URLLC and IoT scheduling, enabling simultaneous advances in efficiency and fairness (Librino et al., 28 Feb 2025);
Assessment and incentivization of open data practices through graph-based transitive metrics that more faithfully reflect scientific reuse than citation counts alone (Sudheendra et al., 17 Nov 2025).

Ongoing research addresses optimization under richer behavioral or environmental uncertainty (Bujak et al., 2022, Wang et al., 20 Dec 2025), integration with dynamic/prioritized queueing (Zhan et al., 2024), and theoretical limits for multi-link and high-dimensional quantum shareability (Mukherjee et al., 2017, Song et al., 2024).

In summary, the shareability-network framework provides a mathematically and algorithmically tractable model for representing and optimizing sharing in a range of domains. It facilitates precise definition of shareability metrics, enables efficient solution of otherwise intractable pooling and assignment problems, and grounds cross-domain policy and protocol design in empirically validated network structure.