T D C C Eight Open Problems in Distributed Computing

Distributed Computing Theory continues to be one of the most active research fields in Theoretical Computer Science today. Besides its foundational topics (such as consensus and synchronization), it is currently being enriched with many new topics inspired from modern technological advances (e.g., the Internet). In this note, we present eight open problems in Distributed Computing Theory that span a wide range of topics – both classical and modern. 1 Wait-Free Consensus A consensus protocol is a distributed algorithm where n processes collectively arrive at a common decision value starting from individual process inputs. It must satisfyagreement(all processes decide on the same value), validity (the decision value is an input to some process), and termination(all processes eventually decide). A protocol in an asynchronous shared-memory system is wait-freeif each process terminates in a finite number of its own steps regardless of scheduling. From the FLP impossibility result [31, 54], wait-free consensus is impossible. However, it becomes possible using randomization with the termination condition relaxed to hold with probability 1. Theopen questionthat then arises is the complexity of solving consensus, measured by the expected number of register operations carried out by all processes (total work) or by any one process ( per-process work ). This complexity depends strongly on assumptions about the power of the adversary scheduler. For an adaptive adversarythat chooses the next process to run based on total knowledge of the current state of the system, the best known protocol using only atomic read-write registers takes O(n2 logn) expected total work [14]. If counters supporting increment, decrement, and read operations are available, this drops to O(n2) expected total work [4]. No faster protocol is known using any objects that can be built from atomic registers, and there is a lower bound ofΩ(n2/ log n) that holds even given powerful tools like unit-cost snapshots [6]. The Bulletin of the EATCS 111 Closing the gap between the upper and lower bounds is interesting because all known polynomial-time wait-free consensus protocols are based on collecting enough random votes that one standard deviation in the total is larger than the n−1 votes that can be “hidden” by the adversary by selectively stopping processes, and it is not hard to show that simple variants on voting cannot yield subquadratic protocols. A faster protocol would thus require a significantly new approach. Conversely, anΩ(n2) lower bound would show that voting is optimal. With a weaker adversary that cannot observe coin flips that have not yet been made public, consensus can be solved in O(logn) work per process using multiwriter registers [11]. There is no corresponding non-trivial lower bound. It would be interesting to see if an Ω(logn) lower bound could be proved for multi-writer registers or even with strong objects like unit-cost snapshots. Closing the gap in both models would show whether the cost of weak-adversary consensus arises from fundamental limitations of grouping local coin-flips together or merely from the weakness of atomic registers.