Upper Bounds for Boundless Tagging with Bounded Objects

Randomized Abortable Mutual Exclusion with Constant Amortized RMR Complexity on the CC Model

“…This naive approach for tagging requires unbounded objects. There are techniques for bounding tags (see e.g., [1]) without increasing step complexity.…”

“…The idea is now that before processes start waiting for S to become (•, unlocked), they get a chance to contact each other and join forces (i.e., share work). To do that, each process p uses a backpack, represented by CAS object B[p] [1]. Initially, the process sets the CAS object to an integer (which is a unique sequence number), meaning the backpack is open.…”

“…We then use a randomized mechanism that gives other processes a chance to discover p, i.e., see that p is participating and has an open backpack. A process b that discovers p tries to write its own ID and a sequence number into B[p] [1] using a CAS() operation (line 16). If that succeeds, b can simply start waiting (in the repeat-until loop in lines [17][18][19][20], and let p do the work.…”

“…If that succeeds, b can simply start waiting (in the repeat-until loop in lines [17][18][19][20], and let p do the work. After each attempt to enter the critical section via "winning" S, process p checks its backpack B[p] [1], and adds the process it found there, if any, to its local set bpack (see method closeBackpacks()). Once process p is critical, it adds all processes collected in bpack during its earlier attempts to win S, to a multiset Q (line 3).…”

“…, n} of n processes communicate by executing atomic operations on shared registers and CAS objects. A compare-and-swap (CAS) object C supports the operations C.read(), which returns the value of C, and C.CAS(old, new), which writes new into C if C = old, and otherwise does not change 1 With atomic we mean that each operation is executed instantaneously.…”