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University of Bergen

Academic institutioneurope · no
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Research library178linked papers
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Selected work

Representative Papers

Path Contraction Faster Than 2n

Jul 08, 2019International Colloquium on Automata, Languages and Programming

This paper addresses the Path Contraction problem: given a graph $G$, determine whether it can be transformed into a path graph $P_k$ of length $k$ via a sequence of edge contractions. A classical graph modification problem, it has long lacked exact algorithms with runtime better than $2^n$. We present the first exact algorithm with runtime $O^*(c^n)$ for some $c < 2$, thereby strictly breaking the exponential base-2 barrier. Our approach introduces the notion of *contraction-sensitive vertices*, integrates structured branching with pruning, graph induction, and dynamic state compression, and employs refined recursive analysis. The theoretical correctness is fully established. The algorithm is deterministic and achieves provable exponential speedup on $n$-vertex graphs. Moreover, our framework yields a generalizable analytical paradigm for broader graph contraction problems.

6 citationsRead paper

Extracting useful information about reversible evolutionary processes from irreversible evolutionary accumulation models

Jan 19, 2026

This study addresses the potential bias introduced by using evolution accumulation models (EvAMs) that assume feature irreversibility when applied to scenarios where true evolutionary processes are reversible. Through comprehensive computer simulations and statistical inference, the authors systematically evaluate how neglecting reversibility affects the reliability of inferred evolutionary event orders and core dynamic structures. The findings reveal that while EvAMs exhibit robustness in reconstructing relative event sequences and backbone pathway architectures, their uncertainty quantification and analyses of feature interactions are notably susceptible to bias stemming from the irreversibility assumption. This work delineates the applicability boundaries and limitations of irreversible EvAMs under reversible evolutionary dynamics, thereby offering both theoretical grounding and practical guidance for modeling evolutionary trajectories.

1 citations1 influentialRead paper

Terminal Coalgebras and Non-wellfounded Sets in Homotopy Type Theory

Jan 18, 2020

This paper addresses the absence of non-well-founded material set models in Homotopy Type Theory (HoTT). We construct, for the first time within HoTT, a semantic model of non-well-founded sets satisfying Scott’s and Aczel’s Anti-Foundation Axioms (SAFA/AFA), based directly on identity types. Our method employs M-types and terminal coalgebras, integrated with propositional truncation and Univalent Material Set Theory, to lift the anti-foundation axioms to higher-type levels; we further provide an exact characterization of indexed M-types in terms of identity types. All results are fully formalized in Agda. Contributions include: (1) the first coalgebraic model of non-well-founded material sets in HoTT; (2) a formal, higher-order generalization of SAFA/AFA and its semantic realization; and (3) a deeper unification of coalgebraic structures with foundational set theory in HoTT.

1 citationsRead paper
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