A Sufficiently Fast Algorithm for Finding Close to Optimal Junction Trees

TL;DR

This paper introduces an efficient algorithm for constructing near-optimal junction trees with bounded clique sizes, enabling polynomial-time inference in Bayesian networks when the largest clique size is logarithmic in the number of vertices.

Contribution

It presents a new algorithm with polynomial complexity for finding nearly optimal junction trees, improving inference efficiency in probabilistic graphical models.

Findings

Algorithm guarantees a near-optimal clique size within a constant factor.

When the largest clique size is logarithmic, the algorithm provides polynomial inference.

The worst-case complexity is polynomial for certain graph classes.

Abstract

An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity O(c^k n^a) where a and c are constants, n is the number of vertices, and k is the size of the largest clique in a junction tree of G in which this size is minimized. The algorithm guarantees that the logarithm of the size of the state space of the heaviest clique in the junction tree produced is less than a constant factor off the optimal value. When k = O(log n), our algorithm yields a polynomial inference algorithm for Bayesian networks.