Srikanth Sastry
Scott M. Pike
ABSTRACT
Dining philosophers is a classic scheduling problem for local mutual exclusion on arbitrary conflict graphs. We establish necessary conditions to solve wait-free dining under eventual weak exclusion in message-passing systems with crash faults. Wait-free dining ensures that every correct hungry process eventually eats. Eventual weak exclusion permits finitely many scheduling mistakes, but eventually no live neighbors eat simultaneously; this exclusion criterion models scenarios where scheduling mistakes are recoverable or only affect performance. Previous work showed that the eventually perfect failure detector (◊P) is sufficient to solve wait-free dining under eventual weak exclusion; we prove that ◊P is also necessary, and thus ◊P is the weakest oracle to solve this problem. Our reduction also establishes that any such dining solution can be made eventually fair. Finally, the reduction itself may be of more general interest; when applied to wait-free perpetual weak exclusion, our reduction produces an alternative proof that the more powerful trusting oracle (T) is necessary (but not sufficient) to solve the problem of Fault-Tolerant Mutual Exclusion (FTME).
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Index Terms
- The weakest failure detector for wait-free dining under eventual weak exclusion
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Reviews
Dana Petcu
Sastry, Pike, and Welch study the classic problem of dining philosophers from a new perspective: the equivalence of wait-free dining, under eventual weak exclusion, with the class of eventually perfect failure detectors. The variant of dining discussed guarantees that every correct process competing for exclusive access to its critical section will eventually access its critical section, in spite of potential process crashes, and that eventually no two live neighbors will be in their critical sections simultaneously. The authors prove that an "eventually perfect failure detector is [necessary and] sufficient to solve wait-free dining under eventual weak exclusion" and, moreover, that it is the weakest oracle to solve this problem. Furthermore, they prove that a certain "powerful trusting oracle is necessary ... to solve the problem of fault-tolerant mutual exclusion." The proofs are carefully described. The paper would be particularly useful to specialists in distributed computing. Online Computing Reviews Service
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