A Back-to-Basics Empirical Study of Priority Queues

Larkin, Daniel H.; Sen, Siddhartha; Tarjan, Robert E.

doi:10.1137/1.9781611973198.7

Cited by 27 publications

(6 citation statements)

References 19 publications

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“…Notice that our complexity analysis in Section 4.4 assumes constant-time inserts for priority queues, which is important for algorithms that push more elements than they pop per iteration. This bound is achieved by data structures that are well-known to perform poorly in practice [44,90]. Instead, we use standard binary heaps for our experiments.…”

Section: Anyk-recmentioning

confidence: 99%

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

Tziavelis¹,

Gatterbauer²,

Riedewald³

2022

Preprint

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We study ranked enumeration for Conjunctive Queries (CQs) where the answers are ordered by a given ranking function (e.g., an ORDER BY clause in SQL). We develop "any-k" algorithms which, without knowing the number 𝑘 of desired answers, push the ranking into joins and avoid materializing the join output earlier than necessary. For this to be possible, the ranking function needs to obey a certain kind of monotonicity; the supported ranking functions include the common sum-of-weights case where query answers are compared by sums of input weights, as well as any commutative selective dioid. One core insight of our work is that the problem is closely related to the fundamental task of path enumeration in a weighted DAG. We generalize and improve upon classic research on finding the 𝑘 th shortest path and unify into the same framework several solutions from different areas that had been studied in isolation. For the time to the 𝑘 th ranked CQ answer (for every value of 𝑘), our approach is optimal in data complexity precisely for the same class of queries where unranked enumeration is optimal-and only slower by a logarithmic factor. In a more careful analysis of combined complexity, we uncover a previously unknown tradeoff between two different any-k algorithms: one has lower complexity when the number of returned results is small, the other when the number is very large. This tradeoff is eliminated under a stricter monotonicity property that we exploit to design a novel algorithm that asymptotically dominates all previously known alternatives, including the well-known algorithm of Eppstein for sum-of-weights path enumeration. We empirically demonstrate the findings of our theoretical analysis in an experimental study that highlights the superiority of our approach over the join-then-rank approach that existing database systems typically follow.

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Section: Anyk-recmentioning

confidence: 99%

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

Tziavelis¹,

Gatterbauer²,

Riedewald³

2022

Preprint

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“…Though log-time in principle these operations are associated with large "hidden" multiplier costs. These additional costs can often slow performance in practice (Larkin, Sen, & Tarjan, 2014), and for this reason implementers often turn to alternative sorting techniques. For example, at the 2014 GPPC several entrants maintain the Open list using a data structure known as a bucket list (Denardo & Fox, 1979;Cazenave, 2006).…”

Section: Maintaining the Open Listmentioning

confidence: 99%

Regarding Goal Bounding and Jump Point Search

Hu¹,

Harabor

Qin

et al. 2021

jair

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Jump Point Search (JPS) is a well known symmetry-breaking algorithm that can substantially improve performance for grid-based optimal pathfinding. When the input grid is static further speedups can be obtained by combining JPS with goal bounding techniques such as Geometric Containers (instantiated as Bounding Boxes) and Compressed Path Databases. Two such methods, JPS+BB and Two-Oracle Path PlannING (Topping), are currently among the fastest known approaches for computing shortest paths on grids. The principal drawback for these algorithms is the overhead costs: each one requires an all-pairs precomputation step, the running time and subsequent storage costs of which can be prohibitive. In this work we consider an alternative approach where we precompute and store goal bounding data only for grid cells which are also jump points. Since the number of jump points is usually much smaller than the total number of grid cells, we can save up to orders of magnitude in preprocessing time and space. Considerable precomputation savings do not necessarily mean performance degradation. For a second contribution we show how canonical orderings, partial expansion strategies and enhanced intermediate pruning can be leveraged to improve online query performance despite a reduction in preprocessed data. The combination of faster preprocessing and stronger online reasoning leads to three new and highly performant algorithms: JPS+BB+ and Two-Oracle Pathfinding Search (TOPS) based on search, and Topping+ based on path extraction. We give a theoretical analysis showing that each method is complete and optimal. We also report convincing gains in a comprehensive empirical evaluation that includes almost all current and cutting-edge algorithms for grid-based pathfinding.

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“…Recent variations of this method, which may further improve performance, are described in (Sturtevant and Rabin 2016). Other related works include studies into alternative search strategies, such as the bi-directional algorithm NBS (Chen et al 2017) -which is sometimes preferable to A * on grids -and studies into more efficient implementations of the OPEN list, such as those evaluated in (Larkin, Sen, and Tarjan 2014).…”

Section: Related Workmentioning

confidence: 99%

Two-Oracle Optimal Path Planning on Grid Maps

Salvetti

Botea²,

Gerevini

et al. 2018

ICAPS

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Path planning on grid maps has progressed significantly in recent years, partly due to the Grid-based Path Planning Competition GPPC. In this work we present an optimal approach which combines features from two modern path planning systems, SRC and JPS+, both of which were among the strongest entrants at the 2014 edition of the competition. Given a current state s and a target state t, SRC is used as an oracle to provide an optimal move from s towards t. Once a direction is available we invoke a second JPS-based oracle to tell us for how many steps that move can be repeated, with no need to query the oracles between these steps. Experiments on a range of grid maps demonstrate a strong improvement from our combined approach. Against SRC, which remains an optimal solver with state-of-the-art speed, the performance improvement of our new system ranges from comparable to more than one order of magnitude faster.

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A Back-to-Basics Empirical Study of Priority Queues

Cited by 27 publications

References 19 publications

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

Regarding Goal Bounding and Jump Point Search

Two-Oracle Optimal Path Planning on Grid Maps

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