This assignment asks students to implement several dynamic programming string-matching algorithms to compare DNA sequences. Since the matching is approximate, their goal is to find the closest match to a given query in a database of known sequences. We use real DNA sequence data to ensure that solutions are reasonably robust. Students get hands-on experience with algorithms they may have only seen on paper and learn about the complex world of approximate string matching, as well as practice working with real-world data. The assignment is appropriate for an upper-level Algorithm Analysis course, where students are learning dynamic programming and algorithm analysis. We use in-person code demonstrations as an opportunity to discuss external factors that affect software engineering beyond just algorithm design, tying abstract algorithm knowledge to real-world concerns and broadening student perspectives.

A multiplicity queue is a concurrently-defined data type which relaxes the conditions of a linearizable FIFO queue by allowing concurrent Dequeue instances to return the same value. It would seem that this should allow faster message-passing implementations, as processes should not need to wait as long to learn about concurrent operations and previous work has shown that multiplicity queues are computationally less complex than the unrelaxed version. Intriguingly, recent work has shown that there is, in fact, little possible speedup versus an unrelaxed queue. Seeking to understand this difference between intuition and real behavior, we increase the lower bound for uniform algorithms. Further, we outline a path toward building proofs for even higher lower bounds, hypothesizing that the worst-case time to Dequeue approaches maximum message delay, which is similar to the time required for an unrelaxed Dequeue. We also give an upper bound for a special case to show that our bounds are tight at that point. To achieve our lower bounds, we use extended shifting arguments, which have been rarely used but allow larger lower bounds than traditional shifting arguments. We use these in series of inductive indistinguishability proofs which allow us to extend our proofs beyond the usual limitations of shifting arguments. This proof structure is an interesting contribution independently of the main result, as developing new lower bound proof techniques may have many uses in future work.

A multiplicity queue is a concurrently-defined data type which relaxes the conditions of a linearizable FIFO queue to allow concurrent Dequeue instances to return the same value. It would seem that this should allow faster implementations, as processes should not need to wait as long to learn about concurrent operations at remote processes and previous work has shown that multiplicity queues are computationally less complex than the unrelaxed version. Intriguingly, recent work has shown that there is, in fact, not much speedup possible versus an unrelaxed queue implementation. Seeking to understand this difference between intuition and real behavior, we extend that work, increasing the lower bound for uniform algorithms. Further, we outline a path forward toward building proofs for even higher lower bounds, allowing us to hypothesize that the worst-case time to Dequeue approaches maximum message delay, which is similar to the time required for an unrelaxed Dequeue. We also give an upper bound for a special case to show that our bounds are tight at that point. To achieve our lower bounds, we use extended shifting arguments, which have been rarely used but allow larger lower bounds than traditional shifting arguments. We use these in series of inductive indistinguishability proofs which allow us to extend our proofs beyond the usual limitations of shifting arguments. This proof structure is an interesting contribution independently of the main result, as developing new lower bound proof techniques may have many uses in future work.

Efficient message-passing implementations of shared data types are a vital component of practical distributed systems, enabling them to work on shared data in predictable ways, but there is a long history of results showing that many of the most useful types of access to shared data are necessarily slow. A variety of approaches attempt to circumvent these bounds, notably weakening consistency guarantees and relaxing the sequential specification of the provided data type. These trade behavioral guarantees for performance. We focus on relaxing the sequential specification of a first-in, first-out queue type, which has been shown to allow faster linearizable implementations than are possible for traditional FIFO queues without relaxation. The algorithms which showed these improvements in operation time tracked a complete execution history, storing complete object state at all n processes in the system, leading to n copies of every stored data element. In this paper, we consider the question of reducing the space complexity of linearizable implementations of shared data types, which provide intuitive behavior through strong consistency guarantees. We improve the existing algorithm for a relaxed queue, showing that it is possible to store only one copy of each element in a shared queue, while still having a low amortized time cost. This is one of several important steps towards making these data types practical in real world systems.

The power of shared data types to solve consensus in asynchronous wait-free systems is a fundamental question in distributed computing, but is largely considered only for specific data types. We consider general classes of abstract shared data types, and classify types of operations on those data types by the knowledge about past operations that processes can extract from the state of the shared object. We prove upper and lower bounds on the number of processes which can use data types in these classes to solve consensus. Our results generalize the consensus numbers known for a wide variety of specific shared data types, such as compare-and-swap, augmented queues and stacks, registers, and cyclic queues. Further, since the classification is based directly on the semantics of operations, one can use the bounds we present to determine the consensus number of a new data type from its specification. We show that, using sets of operations which can detect the first change to the shared object state, or even one at a fixed distance from the beginning of the execution, any number of processes can solve consensus. However, if instead of one of the first changes, operations can only detect one of the most recent changes, then fewer processes can solve consensus. In general, if each operation can either change shared state or read it, but not both, then the number of processes which can solve consensus is limited by the number of consecutive recent operations which can be viewed by a single operation. Allowing operations that both change and read the shared state can allow consensus algorithms with more processes, but if the operations can only see one change a fixed number of operations in the past, we upper bound the number of processes which can solve consensus with a small constant.

Linearizability is a well-known consistency condition for shared objects in concurrent systems. We focus on the problem of implementing linearizable objects of arbitrary data types in message-passing systems with bounded, but uncertain, message delay and bounded, but non-zero, clock skew. We present an algorithm that exploits axiomatic properties of different operations to reduce the running time of each operation below that obtainable with previously known algorithms. We also prove lower bounds on the time complexity of various kinds of operations, specified by the axioms they satisfy, resulting in reduced gaps in some cases and tight bounds in others.