In general this section needs updating. It often reads like its trying to convince the reader that the functionality is worthwhile. Would also benefit from an update to citations in support of capabilities and features. Some text is clunky. Suggestions, corrections, observations, based on MPI 2.1, draft 2008-02-23. 1. p231, line 41: The citation supporting the performance potential of graph defined topologies is from 1989. Are there more recent citations to supplement? Similar question for other citations throughout the chapter. 2. p231, line 47: ³Šwith tremendous benefits for program readability². I appreciate the optimistic tone, but perhaps a little less hype: ³with potential benefitsŠ² 3. p232, line 6: ³The nodes stand forŠ². How about, ³represent²? 4. p232, line 7: ³MPI provides message-passing between any pair of processes in a group.² This seems to imply that topologies are only applicable to point-to-point communication. If so, we should clearly say so, earlier. 5. p232, line 17: Citation [9] is listed as ³To appear.² 6. p232, Lines 23-29. This seems like unnecessary rationalization. Unless it can be substantiated (with a citation), it should be removed. How about, ³When the graph structure is regular and can be completely defined by the number of dimensions and the number of processes in each coordinate direction, such as rings, two- or higher dimensional grids, or tori, a simpler description can be madeŠ² or the like. And then talk about support for Cartesian topologies, which suddenly is mentioned on 6.4, line 3 7. p233, line 5. How about, ³Šare collective, and therefore must adhere to that category¹s requirements.² Clunky, but the ideaŠ 8. p233, line 19: ³Similar functions are contained in EXPRESS and PARMACS.² Can we update (or eliminate) this? Sounds like, ³All the other kids are doing it.² :) 9. p233, line 22-33. Reads clunky. In particular, ³foo can be used toŠ² Implies they are designed primarily for something else. And perhaps provide a high level sentence regarding the content of the paragraph: ³A variety of inquiry functions are provided.² (Which then calls for a bit of a reorganization of the paragraph, since sub-setting functionality is discussed as well. 10. p234, line 27. ³choose a beneficial² rather than ³good². (Could be great! Or ok, orŠ) 11. p237, line 19-20. ³If a topology has been defined with one of the above functionsŠ² How else? Instead: ³Information regarding a process topology can be returned using inquiry functions.² Or something like that. 12. p238, line 6. Is ³dimension² a verb? 13. p241, line 15. I prefer, ³Suppose this topology is associated with communicator comm...² 14. p241, line 34. ³Šan MPI_SENDRECV², since Œa¹ and Œan¹ are selected based on the vowel or consonant sound. Or are these fightin¹ words? :) Errata: 1. pg 237, line 26: (choice) s/b (status). 2. The other errata seems to have been satisfied. Long example, p246. Any verification of correctness available? No complaints in the errata. Richard -- Richard Barrett Future Technologies Group, Computer Science and Mathematics Division, and Scientific Computing Group, National Center for Computational Science Oak Ridge National Laboratory http://ft.ornl.gov/~rbarrett