Institution profile

Aix-Marseille University

Academic institutioneurope · fr
Official website
Research library260linked papers
Opportunities0open roles
Selected work

Representative Papers

Maker-Breaker is solved in polynomial time on hypergraphs of rank 3

Sep 26, 2022

This paper investigates the winner determination problem for Maker-Breaker positional games on 3-uniform hypergraphs. While the problem is PSPACE-complete on general 5-uniform hypergraphs, polynomial-time algorithms were previously known only for two restricted subclasses; Rahman and Watson (2020) conjectured tractability for all 3-uniform hypergraphs. We confirm this conjecture by introducing a “vertex hazard” analytical framework and defining the novel notion of “hazardous subhypergraphs.” We construct a critical family ℱ of hazardous sets and establish a structural characterization: Breaker wins if and only if, at every vertex, all ℱ-hazardous sets pairwise intersect. Based on this, we design the first polynomial-time algorithm for arbitrary 3-uniform hypergraphs, reducing the complexity from PSPACE to P. Furthermore, we prove that if Maker wins, she can achieve her goal within O(log n) moves, and we correct an erroneous claim in recent literature.

7 citations1 influentialRead paper

Impact of knowledge on the cost of treasure hunt in trees

Aug 07, 2021Networks

This paper studies the edge-traversal cost of treasure-hunt tasks by mobile agents on tree networks, focusing on how initial knowledge—specifically, map availability (complete vs. blind) and target-distance awareness (known vs. unknown)—affects worst-case efficiency. Methodologically, it establishes, for the first time, a rigorous partial order among the four knowledge classes; combines deterministic distributed algorithms, graph-traversal analysis, and competitive ratio theory; and derives tight upper and lower bounds on the cost penalty induced by decreasing knowledge precision. Key results show that when distance is known, blind-map traversal incurs significantly higher cost than complete-map traversal; when distance is unknown, the gap narrows substantially; and with a complete map but unknown distance, the cost increase is intermediate. All bounds are tight and constructively achievable. The findings reveal an intrinsic asymmetry in how distance information and map granularity affect efficiency, providing a theoretical benchmark for knowledge–performance trade-offs in distributed search.

3 citationsRead paper

Hardness of monadic second-order formulae over succinct graphs

Feb 09, 2023arXiv.org

This paper classifies the computational complexity of monadic second-order (MSO) logic properties on succinct graphs—Boolean circuits encoding exponentially large graphs. Addressing the failure of Courcelle’s theorem under succinct representations, we establish the first hardness dichotomy for MSO on succinct graphs: every “tree-like” MSO property is either NP-hard or coNP-hard. We rigorously prove that tree-likeness—formalized via bounded treewidth in the circuit encoding—is necessary for this dichotomy; relaxing structural constraints such as cw-nontriviality collapses the dichotomy. Our approach integrates circuit-based graph modeling, semantic analysis of MSO formulas, and parameterized complexity theory. The results not only provide tight lower bounds on the inherent hardness of MSO queries over succinct graphs but also demonstrate that first-order (FO) logic hierarchies similarly lack succinctness robustness. Consequently, the work fundamentally delineates the algorithmic feasibility frontier for logical satisfiability over compact graph representations.

2 citations2 influentialRead paper

Principled model selection for stochastic dynamics

Jan 17, 2025

To address combinatorial explosion and overfitting arising from sparse library selection in stochastic differential equation (SDE) modeling, this paper proposes a parsimonious inference framework integrating likelihood-based statistics and extreme value theory (EVT). The method introduces EVT—novelly applied to SDE model selection—to identify extreme-event thresholds and perform statistical significance tests, thereby suppressing redundant parameters and enabling robust identification of minimal complete models. It unifies maximum likelihood estimation, sparse function library projection, and SDE discretization techniques. Experiments demonstrate that the framework maintains high accuracy under low sampling rates and strong measurement noise, significantly outperforming state-of-the-art methods in ecological network and reaction–diffusion system modeling. By bridging statistical rigor with physical interpretability, it establishes a new paradigm for interpretable modeling of complex stochastic dynamics.

2 citationsRead paper

Adaptive behaviors neutralize bistable explosive transitions in higher-order contagion

Jan 09, 2026

This study investigates how risk-perception-driven adaptive behavior modulates bistable explosive phase transitions in higher-order contagion processes. By integrating numerical simulations with mean-field theory, the authors develop a model in which individuals dynamically adjust their interaction strategies based on local risk perception, and systematically analyze its impact on both pairwise and higher-order transmission dynamics. The findings reveal that such adaptive behavior substantially attenuates the nonlinear effects induced by higher-order interactions, effectively narrowing or even entirely eliminating the parameter regime of bistability. Consequently, the system’s phase transition shifts from explosive to continuous, highlighting the critical role of behavioral feedback in suppressing critical phenomena associated with higher-order contagion.

1 citationsRead paper
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