Distributed Constraint Optimization (DCOP) is a popular framework for cooperative multi-agent decision making. DCOP is NPhard, so an important line of work focuses on developing fast incomplete solution algorithms for large-scale applications. One of the few incomplete algorithms to provide bounds on solution quality is k-size optimality, which defines a local optimality criterion based on the size of the group of deviating agents. Unfortunately, the lack of a general-purpose algorithm and the commitment to forming groups based solely on group size has limited the use of k-size optimality. This paper introduces t-distance optimality which departs from k-size optimality by using graph distance as an alternative criteria for selecting groups of deviating agents. This throws open a new research direction into the tradeoffs between different group selection and coordination mechanisms for incomplete DCOP algorithms. We derive theoretical quality bounds for t-distance optimality that impro...