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Internet coordinate systems (ICS) have been proposed as a method for estimating delays between hosts without direct measurement. However, they can only be accurate when the triangle inequality holds for Internet delays. Actually triangle inequality violations (TIVs) are frequent and are likely to remain a property of the Internet due to routing policies or path inflation. In this paper we propose methods to detect TIVs with high confidence by observing various metrics such as the relative estimation error on the coordinates. Indeed, the detection of TIVs can be used for mitigating their impact on the ICS itself, by excluding some disturbing nodes from clusters running their own ICS, or more generally by improving their neighbor selection mechanism.