Download PDF by Oliver R.: Algebraic Topology, Aarhus 1982: Proceedings of a Conference

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Extra resources for Algebraic Topology, Aarhus 1982: Proceedings of a Conference Held in Aarhus

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Built-In Coloring for Highly-Concurrent Doubly-Linked Lists (Extended Abstract) Hagit Attiya and Eshcar Hillel Department of Computer Science, Technion Abstract. This paper presents a novel approach for lock-free implementations of concurrent data structures, based on dynamically maintaining a coloring of the data structure’s items. Roughly speaking, the data structure’s operations are implemented by acquiring virtual locks on several items of the data structure and then making the changes atomically; this simplifies the design and provides clean functionality.

Therefore, the only new information available to a correct processor by the end of the first round is the identifiers sent by the other two processors. Generally, by the end of r rounds, the processor receives r identifiers from each port. , γr ) be the output of A executed on a processor whose processorID is α, when it gets in round 1 ≤ s ≤ r identifier βs via port 1 and identifier γs via port 2. , γr−1 ) , (1) otherwise in an execution shown in Fig. 3 the correct processors α and β1 decide on the same new id.

An−1 . σn−2 σn ) be a cyclic permutation on n − 1 elements. , an−1 )) . In addition, let D2 be a finite coloring that satisfies D2 (α) = D2 (π(α)) for any α ∈ Zn−1 . Next, we show that the finite coloring D defined by D(α) = (D1 (α), D2 (α)) satisfies (3) for every line in Zn−1 which is parallel to the σ −1 (n)-th axis, with respect to the cyclic permutation π. Since this contradicts the choice of n, this completes the proof. , an−1 ). , aσ−1 (n−1) ). , aσ−1 (n−1) ) ∈ π(L). Moreover aσ−1 (n) = an , since otherwise it holds that π(α) = β, which implies D2 (α) = D2 (β) and thus D(α) = D(β) as well.

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