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Memory latency and bandwidth are significant bottlenecks in designing in-memory indexes. Processing-in-memory (PIM), an emerging hardware design approach, alleviates this problem by embedding processors in memory modules, enabling low-latency memory access whose aggregated bandwidth scales linearly with the number of PIM modules. Despite recent work in balanced comparison-based indexes on PIM systems, building efficient tries for PIMs remains an open challenge due to tries' inherently unbalanced shape. This paper presents the PIM-trie, the first batch-parallel radix-based index for PIM systems that provides load balance and low communication under adversary-controlled workloads. We introduce trie matching-matching a query trie of a batch against the compressed data trie-as a key building block for PIM-friendly index operations. Our algorithm combines (i) hash-based comparisons for coarse-grained work distribution/elimination and (ii) bit-by-bit comparisons for fine-grained matching. Combined with other techniques (meta-block decomposition, selective recursive replication, differentiated verification), PIM-trie supports LongestCommonPrefix, Insert, and Delete in O(logP) communication rounds per batch and O(l/w) communication volume per string, where P is the number of PIM modules, l is the string length in bits, and w is the machine word size. Moreover, work and communication are load-balanced among modules whp, even under worst-case skew. 

The performance of today's in-memory indexes is bottlenecked by the memory latency/bandwidth wall. Processing-in-memory (PIM) is an emerging approach that potentially mitigates this bottleneck, by enabling low-latency memory access whose aggregate memory bandwidth scales with the number of PIM nodes. There is an inherent tension, however, between minimizing inter-node communication and achieving load balance in PIM systems, in the presence of workload skew. This paper presents PIM-tree , an ordered index for PIM systems that achieves both low communication and high load balance, regardless of the degree of skew in data and queries. Our skew-resistant index is based on a novel division of labor between the host CPU and PIM nodes, which leverages the strengths of each. We introduce push-pull search , which dynamically decides whether to push queries to a PIM-tree node or pull the node's keys back to the CPU based on workload skew. Combined with other PIM-friendly optimizations ( shadow subtrees and chunked skip lists ), our PIM-tree provides high-throughput, (guaranteed) low communication, and (guaranteed) high load balance, for batches of point queries, updates, and range scans. We implement PIM-tree, in addition to prior proposed PIM indexes, on the latest PIM system from UPMEM, with 32 CPU cores and 2048 PIM nodes. On workloads with 500 million keys and batches of 1 million queries, the throughput using PIM-trees is up to 69.7X and 59.1x higher than the two best prior PIM-based methods. As far as we know these are the first implementations of an ordered index on a real PIM system. 

We consider a parallel computational model, the Parallel Persistent Memory model, comprised of P processors, each with a fast local ephemeral memory of limited size, and sharing a large persistent memory. The model allows for each processor to fault at any time (with bounded probability), and possibly restart. When a processor faults, all of its state and local ephemeral memory is lost, but the persistent memory remains. This model is motivated by upcoming non-volatile memories that are nearly as fast as existing random access memory, are accessible at the granularity of cache lines, and have the capability of surviving power outages. It is further motivated by the observation that in large parallel systems, failure of processors and their caches is not unusual. We present several results for the model, using an approach that breaks a computation into capsules, each of which can be safely run multiple times. For the single-processor version we describe how to simulate any program in the RAM, the external memory model, or the ideal cache model with an expected constant factor overhead. For the multiprocessor version we describe how to efficiently implement a work-stealing scheduler within the model such that it handles both soft faults, with a processor restarting, and hard faults, with a processor permanently failing. For any multithreaded fork-join computation that is race free, write-after-read conflict free and has W work, D depth, and C maximum capsule work in the absence of faults, the scheduler guarantees a time bound on the model of O(W/P_A+ (DP/P_A ) log_{1/(Cf )} W) in expectation, where P is the maximum number of processors, P_A is the average number, and f ≤ 1/(2C) is the probability a processor faults between successive persistent memory accesses. Within the model, and using the proposed methods, we develop efficient algorithms for parallel prefix sums, merging, sorting, and matrix multiply.