Visualization Biases MLLM's Decision Making in Network Data Tasks

We evaluate how visualizations can influence the judgment of MLLMs about the presence or absence of bridges in a network. We show that the inclusion of visualization improves confidence over a structured text-based input that could theoretically be helpful for answering the question. On the other hand, we observe that standard visualization techniques create a strong bias towards accepting or refuting the presence of a bridge -- independently of whether or not a bridge actually exists in the network. While our results indicate that the inclusion of visualization techniques can effectively influence the MLLM's judgment without compromising its self-reported confidence, they also imply that practitioners must be careful of allowing users to include visualizations in generative AI applications so as to avoid undesired hallucinations.

A Customized SAT-based Solver for Graph Coloring

We introduce ZykovColor, a novel SAT-based algorithm to solve the graph coloring problem working on top of an encoding that mimics the Zykov tree. Our method is based on an approach of H\'ebrard and Katsirelos (2020) that employs a propagator to enforce transitivity constraints, incorporate lower bounds for search tree pruning, and enable inferred propagations. We leverage the recently introduced IPASIR-UP interface for CaDiCal to implement these techniques with a SAT solver. Furthermore, we propose new features that take advantage of the underlying SAT solver. These include modifying the integrated decision strategy with vertex domination hints and using incremental bottom-up search that allows to reuse learned clauses from previous calls. Additionally, we integrate a more efficient clique computation to improve the lower bounds during the search. We validate the effectiveness of each new feature through an experimental analysis. ZykovColor outperforms other state-of-the-art graph coloring implementations on the DIMACS benchmark set. Further experiments on random Erd\H{o}s-R\'enyi graphs show that our new approach dominates state-of-the-art SAT-based methods for both very sparse and highly dense graphs.