arXiv subjects

Kanat Tangwongsan

Publications and source records attributed to Kanat Tangwongsan.

13 recordsLinked to original sources

arXiv2023

Out-of-Order Sliding-Window Aggregation with Efficient Bulk Evictions and Insertions (Extended Version)

Sliding-window aggregation is a foundational stream processing primitive that efficiently summarizes recent data. The state-of-the-art algorithms for sliding-window aggregation are highly efficient when stream data items are evicted or inserted one at a time, even when some of the insertions occur out-of-order. However, real-world streams are often not only out-of-order but also burtsy, causing data items to be evicted or inserted in larger bulks. This paper introduces a new algorithm for sliding-window aggregation with bulk eviction and bulk insertion. For the special case of single insert and evict, our algorithm matches the theoretical complexity of the best previous out-of-order algorithms. For the case of bulk evict, our algorithm improves upon the theoretical complexity of the best previous algorithm for that case and also outperforms it in practice. For the case of bulk insert, there are no prior algorithms, and our algorithm improves upon the naive approach of emulating bulk insert with a loop over single inserts, both in theory and in practice. Overall, this paper makes high-performance algorithms for sliding window aggregation more broadly applicable by efficiently handling the ubiquitous cases of out-of-order data and bursts.

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arXiv2020

In-Order Sliding-Window Aggregation in Worst-Case Constant Time

Sliding-window aggregation is a widely-used approach for extracting insights from the most recent portion of a data stream. The aggregations of interest can usually be expressed as binary operators that are associative but not necessarily commutative nor invertible. Non-invertible operators, however, are difficult to support efficiently. In a 2017 conference paper, we introduced DABA, the first algorithm for sliding-window aggregation with worst-case constant time. Before DABA, if a window had size $n$, the best published algorithms would require $O(\log n)$ aggregation steps per window operation---and while for strictly in-order streams, this bound could be improved to $O(1)$ aggregation steps on average, it was not known how to achieve an $O(1)$ bound for the worst-case, which is critical for latency-sensitive applications. This article is an extended version of our 2017 paper. Besides describing DABA in more detail, this article introduces a new variant, DABA Lite, which achieves the same time bounds in less memory. Whereas DABA requires space for storing $2n$ partial aggregates, DABA Lite only requires space for $n+2$ partial aggregates. Our experiments on synthetic and real data support the theoretical findings.

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arXiv2020

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel batch-dynamic algorithms perform polynomial work per update in the worst case for sparse graphs. In this paper, we present the first work-efficient parallel batch-dynamic algorithm for incremental MST, which can insert $\ell$ edges in $O(\ell \log(1+n/\ell))$ work in expectation and $O(\text{polylog}(n))$ span w.h.p. The key ingredient of our algorithm is an algorithm for constructing a compressed path tree of an edge-weighted tree, which is a smaller tree that contains all pairwise heaviest edges between a given set of marked vertices. Using our batch-incremental MST algorithm, we demonstrate a range of applications that become efficiently solvable in parallel in the sliding-window model, such as graph connectivity, approximate MSTs, testing bipartiteness, $k$-certificates, cycle-freeness, and maintaining sparsifiers.

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arXiv2019

Parallel Streaming Random Sampling

This paper investigates parallel random sampling from a potentially-unending data stream whose elements are revealed in a series of element sequences (minibatches). While sampling from a stream was extensively studied sequentially, not much has been explored in the parallel context, with prior parallel random-sampling algorithms focusing on the static batch model. We present parallel algorithms for minibatch-stream sampling in two settings: (1) sliding window, which draws samples from a prespecified number of most-recently observed elements, and (2) infinite window, which draws samples from all the elements received. Our algorithms are computationally and memory efficient: their work matches the fastest sequential counterpart, their parallel depth is small (polylogarithmic), and their memory usage matches the best known.

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arXiv2018

Streaming k-Means Clustering with Fast Queries

We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster centers while retaining the desirable properties of provably small approximation error and low space usage. Our algorithms rely on a novel idea of "coreset caching" that systematically reuses coresets (summaries of data) computed for recent queries in answering the current clustering query. We present both theoretical analysis and detailed experiments demonstrating their correctness and efficiency

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arXiv2018

Sub-O(log n) Out-of-Order Sliding-Window Aggregation

Sliding-window aggregation summarizes the most recent information in a data stream. Users specify how that summary is computed, usually as an associative binary operator because this is the most general known form for which it is possible to avoid naively scanning every window. For strictly in-order arrivals, there are algorithms with $O(1)$ time per window change assuming associative operators. Meanwhile, it is common in practice for streams to have data arriving slightly out of order, for instance, due to clock drifts or communication delays. Unfortunately, for out-of-order streams, one has to resort to latency-prone buffering or pay $O(\log n)$ time per insert or evict, where $n$ is the window size. This paper presents the design, analysis, and implementation of FiBA, a novel sliding-window aggregation algorithm with an amortized upper bound of $O(\log d)$ time per insert or evict, where $d$ is the distance of the inserted or evicted value to the closer end of the window. This means $O(1)$ time for in-order arrivals and nearly $O(1)$ time for slightly out-of-order arrivals, with a smooth transition towards $O(\log n)$ as $d$ approaches $n$. We also prove a matching lower bound on running time, showing optimality. Our algorithm is as general as the prior state-of-the-art: it requires associativity, but not invertibility nor commutativity. At the heart of the algorithm is a careful combination of finger-searching techniques, lazy rebalancing, and position-aware partial aggregates. We further show how to answer range queries that aggregate subwindows for window sharing. Finally, our experimental evaluation shows that FiBA performs well in practice and supports the theoretical findings.

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arXiv2016

Parallel Shortest-Paths Using Radius Stepping

The single-source shortest path problem (SSSP) with nonnegative edge weights is a notoriously difficult problem to solve efficiently in parallel---it is one of the graph problems said to suffer from the transitive-closure bottleneck. In practice, the $Δ$-stepping algorithm of Meyer and Sanders (J. Algorithms, 2003) often works efficiently but has no known theoretical bounds on general graphs. The algorithm takes a sequence of steps, each increasing the radius by a user-specified value $Δ$. Each step settles the vertices in its annulus but can take $Θ(n)$ substeps, each requiring $Θ(m)$ work ($n$ vertices and $m$ edges). In this paper, we describe Radius-Stepping, an algorithm with the best-known tradeoff between work and depth bounds for SSSP with nearly-linear ($\otilde(m)$) work. The algorithm is a $Δ$-stepping-like algorithm but uses a variable instead of fixed-size increase in radii, allowing us to prove a bound on the number of steps. In particular, by using what we define as a vertex $k$-radius, each step takes at most $k+2$ substeps. Furthermore, we define a $(k, ρ)$-graph property and show that if an undirected graph has this property, then the number of steps can be bounded by $O(\frac{n}ρ \log ρL)$, for a total of $O(\frac{kn}ρ \log ρL)$ substeps, each parallel. We describe how to preprocess a graph to have this property. Altogether, Radius-Stepping takes $O((m+n\log n)\log \frac{n}ρ)$ work and $O(\frac{n}ρ\log n \log (ρL))$ depth per source after preprocessing. The preprocessing step can be done in $O(m\log n + nρ^2)$ work and $O(ρ^2)$ depth or in $O(m\log n + nρ^2\log n)$ work and $O(ρ\log ρ)$ depth, and adds no more than $O(nρ)$ edges.

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arXiv2016

Faster and Simpler Width-Independent Parallel Algorithms for Positive Semidefinite Programming

This paper studies the problem of finding an $(1+ε)$-approximate solution to positive semidefinite programs. These are semidefinite programs in which all matrices in the constraints and objective are positive semidefinite and all scalars are non-negative. We present a simpler \NC parallel algorithm that on input with $n$ constraint matrices, requires $O(\frac{1}{ε^3} log^3 n)$ iterations, each of which involves only simple matrix operations and computing the trace of the product of a matrix exponential and a positive semidefinite matrix. Further, given a positive SDP in a factorized form, the total work of our algorithm is nearly-linear in the number of non-zero entries in the factorization.

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arXiv2016

Work-Efficient Parallel and Incremental Graph Connectivity

On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We present the first shared-memory parallel algorithm for incremental graph connectivity that is both provably work-efficient and has polylogarithmic parallel depth. We also present a simpler algorithm with slightly worse theoretical properties, but which is easier to implement and has good practical performance. Our experiments show a throughput of hundreds of millions of edges per second on a $20$-core machine.

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arXiv2013

Parallel Triangle Counting in Massive Streaming Graphs

The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic, we present the design and implementation of a fast and cache-efficient parallel algorithm for estimating the number of triangles in a massive undirected graph whose edges arrive as a stream. It brings together the benefits of streaming algorithms and parallel algorithms. By building on the streaming algorithms framework, the algorithm has a small memory footprint. By leveraging the paralell cache-oblivious framework, it makes efficient use of the memory hierarchy of modern multicore machines without needing to know its specific parameters. We prove theoretical bounds on accuracy, memory access cost, and parallel runtime complexity, as well as showing empirically that the algorithm yields accurate results and substantial speedups compared to an optimized sequential implementation. (This is an expanded version of a CIKM'13 paper of the same title.)

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arXiv2011

Near Linear-Work Parallel SDD Solvers, Low-Diameter Decomposition, and Low-Stretch Subgraphs

We present the design and analysis of a near linear-work parallel algorithm for solving symmetric diagonally dominant (SDD) linear systems. On input of a SDD $n$-by-$n$ matrix $A$ with $m$ non-zero entries and a vector $b$, our algorithm computes a vector $\tilde{x}$ such that $\norm[A]{\tilde{x} - A^+b} \leq \vareps \cdot \norm[A]{A^+b}$ in $O(m\log^{O(1)}{n}\log{\frac1ε})$ work and $O(m^{1/3+θ}\log \frac1ε)$ depth for any fixed $θ> 0$. The algorithm relies on a parallel algorithm for generating low-stretch spanning trees or spanning subgraphs. To this end, we first develop a parallel decomposition algorithm that in polylogarithmic depth and $\otilde(|E|)$ work, partitions a graph into components with polylogarithmic diameter such that only a small fraction of the original edges are between the components. This can be used to generate low-stretch spanning trees with average stretch $O(n^α)$ in $O(n^{1+α})$ work and $O(n^α)$ depth. Alternatively, it can be used to generate spanning subgraphs with polylogarithmic average stretch in $\otilde(|E|)$ work and polylogarithmic depth. We apply this subgraph construction to derive a parallel linear system solver. By using this solver in known applications, our results imply improved parallel randomized algorithms for several problems, including single-source shortest paths, maximum flow, minimum-cost flow, and approximate maximum flow.

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arXiv2010

Parallel Approximation Algorithms for Facility-Location Problems

This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including $\NC$ and $\RNC$ algorithms for (metric) facility location, $k$-center, $k$-median, and $k$-means. These problems have received considerable attention during the past decades from the approximation algorithms community, concentrating primarily on improving the approximation guarantees. In this paper, we ask, is it possible to parallelize some of the beautiful results from the sequential setting? Our starting point is a small, but diverse, subset of results in approximation algorithms for facility-location problems, with a primary goal of developing techniques for devising their efficient parallel counterparts. We focus on giving algorithms with low depth, near work efficiency (compared to the sequential versions), and low cache complexity. Common in algorithms we present is the idea that instead of picking only the most cost-effective element, we make room for parallelism by allowing a small slack (e.g., a $(1+\vareps)$ factor) in what can be selected---then, we use a clean-up step to ensure that the behavior does not deviate too much from the sequential steps. All the algorithms we developed are ``cache efficient'' in that the cache complexity is bounded by $O(w/B)$, where $w$ is the work in the EREW model and $B$ is the block size.

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arXiv2008

Simpler Analyses of Local Search Algorithms for Facility Location

We study local search algorithms for metric instances of facility location problems: the uncapacitated facility location problem (UFL), as well as uncapacitated versions of the $k$-median, $k$-center and $k$-means problems. All these problems admit natural local search heuristics: for example, in the UFL problem the natural moves are to open a new facility, close an existing facility, and to swap a closed facility for an open one; in $k$-medians, we are allowed only swap moves. The local-search algorithm for $k$-median was analyzed by Arya et al. (SIAM J. Comput. 33(3):544-562, 2004), who used a clever ``coupling'' argument to show that local optima had cost at most constant times the global optimum. They also used this argument to show that the local search algorithm for UFL was 3-approximation; their techniques have since been applied to other facility location problems. In this paper, we give a proof of the $k$-median result which avoids this coupling argument. These arguments can be used in other settings where the Arya et al. arguments have been used. We also show that for the problem of opening $k$ facilities $F$ to minimize the objective function $Φ_p(F) = \big(\sum_{j \in V} d(j, F)^p\big)^{1/p}$, the natural swap-based local-search algorithm is a $Θ(p)$-approximation. This implies constant-factor approximations for $k$-medians (when $p=1$), and $k$-means (when $p = 2$), and an $O(\log n)$-approximation algorithm for the $k$-center problem (which is essentially $p = \log n$).

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