5 research outputs found
A Note on Extreme Sets
In decomposition theory, extreme sets have been studied extensively due to its connection to perfect matchings in a graph. In this paper, we first define extreme sets with respect to degree-matchings and next investigate some of their properties. In particular, we prove the generalized Decomposition Theorem and give a characterization for the set of all extreme vertices in a graph
Gallai-Edmonds decomposition of unicyclic graphs from null space
In this paper, we compute the Gallai-Edmonds decomposition of a unicyclic graph G using linear algebraic tools. More precisely, the Gallai-Edmonds decomposition of G is obtained from the null space associated with adjacency matrices of its subtrees
Quantum-accelerated constraint programming
Constraint programming (CP) is a paradigm used to model and solve constraint
satisfaction and combinatorial optimization problems. In CP, problems are
modeled with constraints that describe acceptable solutions and solved with
backtracking tree search augmented with logical inference. In this paper, we
show how quantum algorithms can accelerate CP, at both the levels of inference
and search. Leveraging existing quantum algorithms, we introduce a
quantum-accelerated filtering algorithm for the global
constraint and discuss its applicability to a broader family of global
constraints with similar structure. We propose frameworks for the integration
of quantum filtering algorithms within both classical and quantum backtracking
search schemes, including a novel hybrid classical-quantum backtracking search
method. This work suggests that CP is a promising candidate application for
early fault-tolerant quantum computers and beyond.Comment: published in Quantu