Efficient approximations for cache-conscious data placement

Abstract

There is a huge and growing gap between the speed of accesses to data stored in main memory vs cache. Thus, cache misses account for a significant portion of runtime overhead in virtually every program and minimizing them has been an active research topic for decades. The primary and most classical formal model for this problem is that of Cacheconscious Data Placement (CDP): given a commutative cache with constant capacity 𝑘 and a sequence Σ of accesses to data elements, the goal is to map each data element to a cache line such that the total number of cache misses over Σ is minimized. Note that we are considering an offline singlethreaded setting in which Σ is known a priori. CDP has been widely studied since the 1990s. In POPL 2002, Petrank and Rawitz proved a notoriously strong hardness result: They showed that for every 𝑘 ≥ 3, CDP is not only NP-hard but also hard-to-approximate within any non-trivial factor unless P = NP. As such, all subsequent works gave up on theoretical improvements and instead focused on heuristic algorithms with no theoretical guarantees.In this work, we present the first-ever positive theoretical result for CDP. The fundamental idea behind our approach is that real-world instances of the problem have specific structural properties that can be exploited to obtain efficient

Efficient Interprocedural Data-Flow Analysis Using Treedepth and Treewidth

“…The theoretical bound of [78] does not apply to Java, but the work [44] showed that the treewidth of control-flow graphs in real-world Java programs is also bounded. This bounded-treewidth property has been used in a variety of static analysis and compiler optimization tasks to speed up the underlying algorithms [25,62,3,27,36,26,20,23,5,38,2]. Nevertheless, one can theoretically construct pathological examples with high treewidth.…”

“…It is proven that structured programs in several languages, such as C, have bounded treewidth [78] and there are experimental works that establish small bounds on the treewidth of control-flow graphs of real-world programs written in other languages, such as Java [44], Ada [16] and Solidity [19]. Using these facts, [22] provides an ondemand algorithm with O(n • |D| 3 ) preprocessing time and O ⌈ |D| lg n ⌉ time per query 2 . In practice, |D| is often tiny in comparison with n and hence this algorithm is considered to have linear preprocessing and constant query time.…”

A Novel Data Management Scheme in Cloud for Micromachines

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