Existing Large Language Model (LLM) routing methods score LLMs independently to select top-$k$ models. However, this ignores model correlations and enforces a rigid computational budget.
Consequently, routers often select redundant models that share failure modes, limiting the overall probability of success.
To address this, we propose FlexRouter, a routing framework that explicitly models model complementarity.
FlexRouter optimizes for answer coverage, maximizing the probability that at least one selected model yields a correct response.
This objective aligns with practical inference pipelines where multiple candidate outputs are generated and a downstream verifier or user selects the final one.
We formulate routing as a coverage-oriented subset selection problem and model the routing policy using Determinantal Point Processes (DPPs), which naturally capture both model competence and redundancy.
To directly optimize coverage without requiring a ground-truth target subset, we introduce a training objective based on marginalizing over failure sets.
During inference, we employ a greedy strategy based on marginal log-determinant gains, enabling the router to adaptively determine subset sizes without a predefined budget.
Extensive experiments on the large-scale RouterEval benchmark demonstrate that our proposed FlexRouter achieves higher coverage with lower redundancy across both in-domain and out-of-domain tasks than strong baselines while maintaining flexible inference cost.