We investigate scheduling algorithms for distributed transactional memory systems where transactions residing at nodes of a communication graph operate on shared, mobile objects. A transaction requests the objects it needs, executes once those objects have been assembled, and then possibly forwards those objects to other waiting transactions. Minimizing execution time in this model is known to be NP-hard for arbitrary communication graphs, and also hard to approximate within any factor smaller than the size of the graph. Nevertheless, networks on chips, multi-core systems, and clusters are not arbitrary. Here, we explore efficient execution schedules in specialized graphs likely to arise in practice: Clique, Line, Grid, Cluster, Hypercube, Butterfly, and Star. In most cases, when individual transactions request k objects, we obtain solutions close to a factor O(k) from optimal, yielding near-optimal solutions for constant k. These execution times approximate the TSP tour lengths of the objects in the graph. We show that for general networks, even for two objects (k = 2), it is impossible to obtain execution time close to the objects' optimal TSP tour lengths, which is why it is useful to consider more realistic network models. To our knowledge, this is the first a.empt to obtain provably fast schedules for distributed transactional memory.