arXiv subjects

Guy E. Blelloch

Publications and source records attributed to Guy E. Blelloch.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic Entropy-Encoded Arrays in O(1) Time with Nearly Optimal Space

We show how to implement a dynamic array $A[1, n]$ with symbols from a fixed alphabet $Σ$, while supporting $O(1)$-time queries and updates, and using a total space of $$ \log \binom{|Σ|}{m} + \left(1 + O\left(\frac{\log \log n}{\log n}\right)\right) \cdot \left(\sum_{σ\in Σ} f_σ\log (n / f_σ)\right) + n / \text{polylog } n $$ bits, where $f_σ$ denotes the frequency of each symbol $σ\in Σ$ and $m$ denotes the number of distinct symbols with non-zero frequencies. This resolves a long-standing open question as to whether one can achieve space bounds close to that of arithmetic coding, while supporting $O(1)$-time operations, whenever the entropy is at least $n/\text{polylog } n$. We also prove a nearly matching space lower bound: up to a factor of $O(\log \log n)$, the entropy-dependent multiplicative overhead of our construction is optimal among $O(1)$-time solutions when $|Σ|=O(\sqrt n)$ and the entropy $\sum_{σ\in Σ} f_σ\log (n / f_σ)$ lies between $n/\log^{O(1)}n$ and $(1/100)n\log n$. Finally, we present several applications of our results, resolving two open problems having to do with space-efficient dictionaries and filters.

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arXiv2026

Optimal Time-Space Tradeoff for Dynamic Difference-Encoded Dictionaries

The dynamic dictionary is a fundamental data structure that maintains a set $S\subset [U]$ of size $n$ (we assume $n=U^{1-Θ(1)}$), supporting insertions, deletions and membership queries. Previous works mostly focused on constructing dictionaries that support operations in $O(1)$ time and use space as close to the \emph{information-theoretic bound} of $\log\binom{U}{n}$ bits as possible. In this paper, we study \emph{difference-encoded} dictionaries, which are dictionaries that use space close to the gap entropy $\text{gap}(S):=\sum_{i=2}^{|S|}\left(\lceil\log(x_i-x_{i-1}+1)\rceil+1\right)$ bits to store the set $S=\{x_1<\dots<x_n\}$. On many real-world datasets where the keys are clustered, we have $\text{gap}(S)\ll \log\binom{U}{n}$, making difference-encoded dictionaries more favorable than standard dictionaries in practice. Prior to this work, the best dynamic difference-encoded dictionary is by Blandford and Blelloch [SODA'04], whose construction supports operations in $O(\log n)$ time and uses $O(\text{gap}(S))$ bits of space. In the static case, Gupta, Hon, Shah and Vitter [DCC'06] presented a dictionary that uses $$ \text{gap}(S)+O(n\log\log U) $$ bits of space and supports membership queries in $O(\log\log n)$ time. In this work, we go beyond these bounds and fully settle the optimal time-space tradeoff for difference-encoded dictionaries. For an arbitrary parameter $0<\varepsilon<1/4$, we construct a dynamic dictionary that supports operations in $O(\log\varepsilon^{-1}/\log\log\varepsilon^{-1})$ expected amortized time and uses $$ \text{gap}(S)\cdot(1+O(\varepsilon))+O\left(n\log\frac{\text{gap}(S)}{n}\right) $$ bits of space. We also prove a matching lower bound, showing that our time-space tradeoff is optimal even in the \emph{static} case.

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arXiv2026

TD-Orch: Efficient Task-Data Orchestration for Distributed Systems with Application to Graph Processing

We introduce a task-data orchestration abstraction that supports a range of distributed applications. Given a batch of lambda tasks each requesting a data item, where both tasks and data are distributed across multiple machines, each task must be co-located with its target data (by moving tasks and/or data) and then executed. We present TD-Orch, an efficient lambda-task-centric orchestration framework for low-overhead load balancing with a simple interface for application developers. TD-Orch employs a distributed push-pull technique, leveraging the bidirectional flow of both tasks and data to achieve load balance across machines even under highly skewed access patterns, with low communication overhead. Experimental results on key-value stores show that TD-Orch achieves up to $2.8\times$ speedup over existing distributed scheduling baselines. Building on TD-Orch, we present TDO-GP, a distributed graph processing system with $4.1\times$ average speedup over state-of-the-art open-source distributed graph systems for general graph processing.

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arXiv2026

Fast Concurrent Primitives Despite Contention

We study the problem of constructing concurrent objects in a setting where $P$ processes run in parallel and interact through a shared memory that is subject to write contention. Our goal is to transform hardware primitives that are subject to write contention into ones that handle contention gracefully. We give contention-resolution algorithms for several basic primitives, and analyze them under a relaxed, roughly-synchronous stochastic scheduler, where processes run at roughly the same rate up to a constant factor with high probability. Specifically, we construct read/write registers and CAS registers that have latency $O(\log P)$ w.h.p. under our scheduler model, using $O(1)$ hardware read/write registers and, in the case of our CAS construction, one hardware CAS register. Our algorithms guarantee performance even when their operations are invoked by an adaptive adversary that is able to see the entire history of operations so far, including their timing and return values. This allows them to be used as building blocks inside larger programs; using this compositionality property, we obtain several other constructions (LL/SC, fetch-and-increment, bounded max registers, and counters). To complement our constructions, we give a trade-off showing that even under a perfectly synchronous schedule and even if each process only executes one operation, any algorithm that implements any of the primitives that we consider, uses space $M$, and has latency at most $L$ with high probability must have expected latency at least $Ω(\log_{ML} P)$.

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arXiv2025

Parallel Batch-Dynamic Maximal Matching with Constant Work per Update

We present a work optimal algorithm for parallel fully batch-dynamic maximal matching against an oblivious adversary. It processes batches of updates (either insertions or deletions of edges) in constant expected amortized work per edge update, and in $O(\log^3 m)$ depth per batch whp, where $m$ is the maximum number of edges in the graph over time. This greatly improves on the recent result by Ghaffari and Trygub (2024) that requires $O(\log^9 m)$ amortized work per update and $O(\log^4 m )$ depth per batch, both whp. The algorithm can also be used for parallel batch-dynamic hyperedge maximal matching. For hypergraphs with rank $r$ (maximum cardinality of any edge) the algorithm supports batches of updates with $O(r^3)$ expected amortized work per edge update, and $O(\log^3 m)$ depth per batch whp. Ghaffari and Trygub's parallel batch-dynamic algorithm on hypergraphs requires $O(r^8 \log^9 m)$ amortized work per edge update whp. We leverage ideas from the prior algorithms but introduce substantial new ideas. Furthermore, our algorithm is relatively simple, perhaps even simpler than Assadi and Solomon's (2021) sequential dynamic hyperedge algorithm. We also present the first work-efficient algorithm for parallel static maximal matching on hypergraphs. For a hypergraph with total cardinality $m'$ (i.e., sum over the cardinality of each edge), the algorithm runs in $O(m')$ work in expectation and $O(\log^2 m)$ depth whp. The algorithm also has some properties that allow us to use it as a subroutine in the dynamic algorithm to select random edges in the graph to add to the matching. With a standard reduction from set cover to hyperedge maximal matching, we give state of the art $r$-approximate static and batch-dynamic parallel set cover algorithms, where $r$ is the maximum frequency of any element, and batch-dynamic updates consist of adding or removing batches of elements.

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arXiv2025

Range Retrieval with Graph-Based Indices

Retrieving points based on proximity in a high-dimensional vector space is a crucial step in information retrieval applications. The approximate nearest neighbor search (ANNS) problem, which identifies the $k$ nearest neighbors for a query, has been extensively studied in recent years. However, comparatively little attention has been paid to the related problem of finding all points within a given distance of a query, the range retrieval problem, despite its applications in areas such as duplicate detection, plagiarism checking, and facial recognition. In this paper, we present new techniques for range retrieval on graph-based vector indices, which are known to achieve excellent performance on ANNS queries. Since a range query may have anywhere from no matching results to thousands of matching results in the database, we introduce a set of range retrieval algorithms based on modifications of the standard graph search that adapt to terminate quickly on queries in the former group, and to put more resources into finding results for the latter group. Due to the lack of existing benchmarks for range retrieval, we also undertake a comprehensive study of range characteristics of existing embedding datasets, and select a suitable range retrieval radius for eight existing datasets with up to 1 billion points in addition to one existing benchmark. We test our algorithms on these datasets, and find up to 100x improvement in query throughput over a standard graph search and the FAISS-IVF range search algorithm. We also find up to 10x improvement over a previously suggested modification of the standard beam search, and strong performance up to 1 billion data points.

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arXiv2025

Big Atomics

In this paper, we give theoretically and practically efficient implementations of Big Atomics, i.e., $k$-word linearizable registers that support the load, store, and compare-and-swap (CAS) operations. While modern hardware supports $k = 1$ and sometimes $k = 2$ (e.g., double-width compare-and-swap in x86), our implementations support arbitrary $k$. Big Atomics are useful in many applications, including atomic manipulation of tuples, version lists, and implementing load-linked/store-conditional (LL/SC). We design fast, lock-free implementations of big atomics based on a novel fast-path-slow-path approach we develop. We then use them to develop an efficient concurrent hash table, as evidence of their utility. We experimentally validate the approach by comparing a variety of implementations of big atomics under a variety of workloads (thread counts, load/store ratios, contention, oversubscription, and number of atomics). The experiments compare two of our lock-free variants with C++ std::atomic, a lock-based version, a version using sequence locks, and an indirect version. The results show that our approach is close to the fastest under all conditions and far outperforms others under oversubscription. We also compare our big atomics based concurrent hash table to a variety of other state-of-the-art hash tables that support arbitrary length keys and values, including implementations from Intel's TBB, Facebook's Folly, libcuckoo, and a recent release from Boost. The results show that our approach of using big atomics in the design of hash tables is a promising direction.

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arXiv2024

ParlayANN: Scalable and Deterministic Parallel Graph-Based Approximate Nearest Neighbor Search Algorithms

Approximate nearest-neighbor search (ANNS) algorithms are a key part of the modern deep learning stack due to enabling efficient similarity search over high-dimensional vector space representations (i.e., embeddings) of data. Among various ANNS algorithms, graph-based algorithms are known to achieve the best throughput-recall tradeoffs. Despite the large scale of modern ANNS datasets, existing parallel graph based implementations suffer from significant challenges to scale to large datasets due to heavy use of locks and other sequential bottlenecks, which 1) prevents them from efficiently scaling to a large number of processors, and 2) results in nondeterminism that is undesirable in certain applications. In this paper, we introduce ParlayANN, a library of deterministic and parallel graph-based approximate nearest neighbor search algorithms, along with a set of useful tools for developing such algorithms. In this library, we develop novel parallel implementations for four state-of-the-art graph-based ANNS algorithms that scale to billion-scale datasets. Our algorithms are deterministic and achieve high scalability across a diverse set of challenging datasets. In addition to the new algorithmic ideas, we also conduct a detailed experimental study of our new algorithms as well as two existing non-graph approaches. Our experimental results both validate the effectiveness of our new techniques, and lead to a comprehensive comparison among ANNS algorithms on large scale datasets with a list of interesting findings.

cs.IR↗

arXiv2023

Deterministic and Work-Efficient Parallel Batch-Dynamic Trees in Low Span

Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge insertions and deletions while answering queries about the tree, such as the heaviest weight on a path, etc. In the parallel batch-dynamic setting, the goal is to process batches of edge updates work efficiently in low ($\text{polylog}\ n$) span. Two work-efficient algorithms are known, batch-parallel Euler Tour Trees by Tseng et al. [ALENEX'19, (2019), pp. 92-106] and parallel Rake-Compress (RC) Trees by Acar et al. [ESA'20, (2020), pp. 2:1-2:23]. Both however are randomized and work efficient in expectation. Several downstream results that use these data structures (and indeed to the best of our knowledge, all known work-efficient parallel batch-dynamic graph algorithms) are therefore also randomized. In this work, we give the first deterministic work-efficient solution to the problem. Our algorithm maintains a dynamic parallel tree contraction subject to batches of $k$ edge updates deterministically in worst-case $O(k \log(1 + n/k))$ work and $O(\log n \log^{(c)} k)$ span for any constant $c$. This allows us to implement parallel batch-dynamic RC-Trees with worst-case $O(k \log(1 + n/k))$ work updates and queries deterministically. Our techniques that we use to obtain the given span bound can also be applied to the state-of-the-art randomized variant of the algorithm to improve its span from $O(\log n \log^* n)$ to $O(\log n)$.

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arXiv2023

Practically and Theoretically Efficient Garbage Collection for Multiversioning

Multiversioning is widely used in databases, transactional memory, and concurrent data structures. It can be used to support read-only transactions that appear atomic in the presence of concurrent update operations. Any system that maintains multiple versions of each object needs a way of efficiently reclaiming them. We experimentally compare various existing reclamation techniques by applying them to a multiversion tree and a multiversion hash table. Using insights from these experiments, we develop two new multiversion garbage collection (MVGC) techniques. These techniques use two novel concurrent version list data structures. Our experimental evaluation shows that our fastest technique is competitive with the fastest existing MVGC techniques, while using significantly less space on some workloads. Our new techniques provide strong theoretical bounds, especially on space usage. These bounds ensure that the schemes have consistent performance, avoiding the very high worst-case space usage of other techniques.

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arXiv2022

PIM-tree: A Skew-resistant Index for Processing-in-Memory

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 the data and the queries. Our skew-resistant index is based on a novel division of labor between the multi-core host CPU and the 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 (CPU -> PIM-node) or pull the node's keys back to the CPU (PIM-node -> 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 the PIM-tree structure, 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 one million queries, the throughput using PIM-trees is up to 69.7x and 59.1x higher than the two best prior methods. As far as we know these are the first implementations of an ordered index on a real PIM system.

cs.DB↗

arXiv2022

Fast and Fair Randomized Wait-Free Locks

We present a randomized approach for wait-free locks with strong bounds on time and fairness in a context in which any process can be arbitrarily delayed. Our approach supports a tryLock operation that is given a set of locks, and code to run when all the locks are acquired. A tryLock operation, or attempt, may fail if there is contention on the locks, in which case the code is not run. Given an upper bound $κ$ known to the algorithm on the point contention of any lock, and an upper bound $L$ on the number of locks in a tryLock's set, a tryLock will succeed in acquiring its locks and running the code with probability at least $1/(κL)$. It is thus fair. Furthermore, if the maximum step complexity for the code in any lock is $T$, the attempt will take $O(κ^2 L^2 T)$ steps, regardless of whether it succeeds or fails. The attempts are independent, thus if the tryLock is repeatedly retried on failure, it will succeed in $O(κ^3 L^3 T)$ expected steps, and with high probability in not much more.

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arXiv2022

Turning Manual Concurrent Memory Reclamation into Automatic Reference Counting

Safe memory reclamation (SMR) schemes are an essential tool for lock-free data structures and concurrent programming. However, manual SMR schemes are notoriously difficult to apply correctly, and automatic schemes, such as reference counting, have been argued for over a decade to be too slow for practical purposes. A recent wave of work has disproved this long-held notion and shown that reference counting can be as scalable as hazard pointers, one of the most common manual techniques. Despite these tremendous improvements, there remains a gap of up to 2x or more in performance between these schemes and faster manual techniques such as epoch-based reclamation (EBR). In this work, we first advance these ideas and show that in many cases, automatic reference counting can in fact be as fast as the fastest manual SMR techniques. We generalize our previous Concurrent Deferred Reference Counting (CDRC) algorithm to obtain a method for converting any standard manual SMR technique into an automatic reference counting technique with a similar performance profile. Our second contribution is extending this framework to support weak pointers, which are reference-counted pointers that automatically break pointer cycles by not contributing to the reference count, thus addressing a common weakness in reference-counted garbage collection. Our experiments with a C++-library implementation show that our automatic techniques perform in line with their manual counterparts, and that our weak pointer implementation outperforms the best known atomic weak pointer library by up to an order of magnitude on high thread counts. All together, we show that the ease of use of automatic memory management can be achieved without significant cost to practical performance or general applicability.

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arXiv2022

PaC-trees: Supporting Parallel and Compressed Purely-Functional Collections

Many modern programming languages are shifting toward a functional style for collection interfaces such as sets, maps, and sequences. Functional interfaces offer many advantages, including being safe for parallelism and providing simple and lightweight snapshots. However, existing high-performance functional interfaces such as PAM, which are based on balanced purely-functional trees, incur large space overheads for large-scale data analysis due to storing every element in a separate node in a tree. This paper presents PaC-trees, a purely-functional data structure supporting functional interfaces for sets, maps, and sequences that provides a significant reduction in space over existing approaches. A PaC-tree is a balanced binary search tree which blocks the leaves and compresses the blocks using arrays. We provide novel techniques for compressing and uncompressing the blocks which yield practical parallel functional algorithms for a broad set of operations on PaC-trees such as union, intersection, filter, reduction, and range queries which are both theoretically and practically efficient. Using PaC-trees we designed CPAM, a C++ library that implements the full functionality of PAM, while offering significant extra functionality for compression. CPAM consistently matches or outperforms PAM on a set of microbenchmarks on sets, maps, and sequences while using about a quarter of the space. On applications including inverted indices, 2D range queries, and 1D interval queries, CPAM is competitive with or faster than PAM, while using 2.1--7.8x less space. For static and streaming graph processing, CPAM offers 1.6x faster batch updates while using 1.3--2.6x less space than the state-of-the-art graph processing system Aspen.

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arXiv2022

Lock-Free Locks Revisited

This paper presents a new and practical approach to lock-free locks based on helping, which allows the user to write code using fine-grained locks, but run it in a lock-free manner. Although lock-free locks have been suggested in the past, they are widely viewed as impractical, have some key limitations, and, as far as we know, have never been implemented. The paper presents some key techniques that make lock-free locks practical and more general. The most important technique is an approach to idempotence -- i.e. making code that runs multiple times appear as if it ran once. The idea is based on using a shared log among processes running the same protected code. Importantly, the approach can be library based, requiring very little if any change to standard code -- code just needs to use the idempotent versions of memory operations (load, store, LL/SC, allocation, free). We have implemented a C++ library called Flock based on the ideas. Flock allows lock-based data structures to run in either lock-free or blocking (traditional locks) mode. We implemented a variety of tree and list-based data structures with Flock and compare the performance of the lock-free and blocking modes under a variety of workloads. The lock-free mode is almost as fast as blocking mode under almost all workloads, and significantly faster when threads are oversubscribed (more threads than processors). We also compare with several existing lock-based and lock-free alternatives.

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arXiv2021

Parallel Minimum Cuts in $O(m \log^2(n))$ Work and Low Depth

We present a randomized $O(m \log^2 n)$ work, $O(\text{polylog } n)$ depth parallel algorithm for minimum cut. This algorithm matches the work bounds of a recent sequential algorithm by Gawrychowski, Mozes, and Weimann [ICALP'20], and improves on the previously best parallel algorithm by Geissmann and Gianinazzi [SPAA'18], which performs $O(m \log^4 n)$ work in $O(\text{polylog } n)$ depth. Our algorithm makes use of three components that might be of independent interest. Firstly, we design a parallel data structure that efficiently supports batched mixed queries and updates on trees. It generalizes and improves the work bounds of a previous data structure of Geissmann and Gianinazzi and is work efficient with respect to the best sequential algorithm. Secondly, we design a parallel algorithm for approximate minimum cut that improves on previous results by Karger and Motwani. We use this algorithm to give a work-efficient procedure to produce a tree packing, as in Karger's sequential algorithm for minimum cuts. Lastly, we design an efficient parallel algorithm for solving the minimum $2$-respecting cut problem.

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arXiv2021

Space and Time Bounded Multiversion Garbage Collection

We present a general technique for garbage collecting old versions for multiversion concurrency control that simultaneously achieves good time and space complexity. Our technique takes only $O(1)$ time on average to reclaim each version and maintains only a constant factor more versions than needed (plus an additive term). It is designed for multiversion schemes using version lists, which are the most common. Our approach uses two components that are of independent interest. First, we define a novel range-tracking data structure which stores a set of old versions and efficiently finds those that are no longer needed. We provide a wait-free implementation in which all operations take amortized constant time. Second, we represent version lists using a new lock-free doubly-linked list algorithm that supports efficient (amortized constant time) removals given a pointer to any node in the list. These two components naturally fit together to solve the multiversion garbage collection problem--the range-tracker identifies which versions to remove and our list algorithm can then be used to remove them from their version lists. We apply our garbage collection technique to generate end-to-end time and space bounds for the multiversioning system of Wei et al. (PPoPP 2021).

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arXiv2021

NVTraverse: In NVRAM Data Structures, the Destination is More Important than the Journey

The recent availability of fast, dense, byte-addressable non-volatile memory has led to increasing interest in the problem of designing and specifying durable data structures that can recover from system crashes. However, designing durable concurrent data structures that are efficient and also satisfy a correctness criterion has proven to be very difficult, leading many algorithms to be inefficient or incorrect in a concurrent setting. In this paper, we present a general transformation that takes a lock-free data structure from a general class called traversal data structure (that we formally define) and automatically transforms it into an implementation of the data structure for the NVRAM setting that is provably durably linearizable and highly efficient. The transformation hinges on the observation that many data structure operations begin with a traversal phase that does not need to be persisted, and thus we only begin persisting when the traversal reaches its destination. We demonstrate the transformation's efficiency through extensive measurements on a system with Intel's recently released Optane DC persistent memory, showing that it can outperform competitors on many workloads.

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