Dominating Set Algorithms in Social Network Analysis

The concept of a dominating set occupies a central place in graph-theoretic approaches to social network analysis. A dominating set is a subset of actors such that every individual outside this set has a direct tie to at least one member within it. In social contexts, nodes in the dominating set often correspond to influencers, key communicators or control points that facilitate information propagation, resource allocation and monitoring tasks. Determining a minimum dominating set – that is, the smallest possible such subset – is an NP-hard combinatorial problem, spurring the development of a diverse array of exact, approximation and heuristic methods. Greedy strategies form a foundation, iteratively selecting nodes that maximise newly dominated neighbours, while more sophisticated metaheuristics combine greedy initialisation with local search, cross-entropy sampling or learning-based updates. Centrality-driven frameworks integrate measures such as degree, betweenness or novel two-level centralities to guide selection in large-scale networks. Modern work emphasises resilience under node removal, positive-influence variants to model cascades of behavioural adoption and flexible algorithms that balance domination coverage against fault tolerance. These advances underpin applications from viral marketing and epidemic containment to robust sensor deployment and critical infrastructure oversight, highlighting the global significance of dominating set algorithms in dissecting and engineering social connectivity.

Research from Nature Portfolio

Recent work has focused on the resilience of dominating sets in the face of random and targeted node failures. It has been demonstrated that cost-efficient dominating sets optimised solely for size can be disproportionately vulnerable to even minor disruptions. To mitigate this, two new methodologies introduce flexible dominating sets that allow an adjustable trade-off between set size and post-attack coverage. One method adapts the selection process to prioritise nodes with redundant coverage, while the other dynamically reconfigures the set after failures to maximise the fraction of the network that remains dominated. These approaches have been tested on synthetic scale-free models and real complex networks, revealing improved robustness against both random removals and deliberate attacks and offering practical guidance for maintaining control and observability in social and infrastructural graphs.

Research from all publishers

Among algorithms developed outside the portfolio, an iterated greedy metaheuristic has shown remarkable efficacy in large-scale graphs. This technique alternates between greedy selection and controlled perturbations to escape local optima, achieving near-optimal domination numbers with deviations below 1.3% in challenging benchmarks. Another strand exploits domain-specific objectives, exemplified by positive-influence dominating sets that identify minimal groups of influential agents to trigger global behavioural adoption. Fast greedy heuristics tailored to this variant outperform integer-linear programming solvers on large networks, while retaining competitive performance on small to medium instances. Recent innovations also integrate centrality metrics in dynamic greedy frameworks, using multi-level centrality weights to prioritise nodes that balance influence potential and redundancy. Such algorithms scale effectively to graphs with millions of vertices, demonstrating practical viability for real-world social platforms and collaborative systems.

Dominating Set Algorithms in Social Network Analysis publication trend

The graph below shows the total number of articles in dominating set algorithms in social network analysis across all publications each year (not limited to Nature Index journals).

Technical terms

Dominating set: A vertex subset such that every node not in the subset is adjacent to at least one member.

Domination number: The minimum cardinality of a dominating set in a graph.

Greedy algorithm: A heuristic that iteratively selects the locally optimal choice, such as the node covering the most undominated neighbours.

Metaheuristic: A higher-level procedure, often combining greedy strategies with local search or stochastic sampling to improve solutions.

Centrality measure: A metric (e.g., degree, betweenness) quantifying a node’s structural importance within a network.

NP-hard: A classification denoting problems for which no polynomial-time algorithm is known.

References

1. An iterated greedy algorithm for finding the minimum dominating set in graphs. Mathematics and Computers in Simulation (2023).
2. An Improved Greedy Heuristic for the Minimum Positive Influence Dominating Set Problem in Social Networks. Algorithms (2021).
3. Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks. Scientific Reports (2015).
4. A Cross-Entropy Approach to the Domination Problem and Its Variants. Entropy (2024).