Failures and anomalies in large-scale software systems are unavoidable incidents. When an issue is detected, operators need to quickly and correctly identify its location to facilitate a swift repair. In this work, we consider the problem of identifying the root cause set that best explains an anomaly in multi-dimensional time series with categorical attributes. The huge search space is the main challenge, even for a small number of attributes and small value sets, the number of theoretical combinations is too large to brute force. Previous approaches have thus focused on reducing the search space, but they all suffer from various issues, requiring extensive manual parameter tuning, being too slow and thus impractical, or being incapable of finding more complex root causes. We propose RiskLoc to solve the problem of multidimensional root cause localization. RiskLoc applies a 2-way partitioning scheme and assigns element weights that linearly increase with the distance from the partitioning point. A risk score is assigned to each element that integrates two factors, 1) its weighted proportion within the abnormal partition, and 2) the relative change in the deviation score adjusted for the ripple effect property. Extensive experiments on multiple datasets verify the effectiveness and efficiency of RiskLoc, and for a comprehensive evaluation, we introduce three synthetically generated datasets that complement existing datasets. We demonstrate that RiskLoc consistently outperforms state-of-the-art baselines, especially in more challenging root cause scenarios, with gains in F1-score up to 57% over the second-best approach with comparable running times.