Time-space Tradeoff Research Articles

A time–space trade-off for computing the k-visibility region of a point in a polygon

Let P be a simple polygon with n vertices, and let q∈P be a point in P. Let k∈{0,…,n−1}. A point p∈P is k-visible from q if and only if the line segment pq crosses the boundary of P at most k times. The k-visibility region of q in P is the set of all points that are k-visible from q. We study the problem of computing the k-visibility region in the limited workspace model, where the input resides in a random-access read-only memory of O(n) words, each with Ω(log⁡n) bits. The algorithm can read and write O(s) additional words of workspace, where s∈N is a parameter of the model. The output is written to a write-only stream.Given a simple polygon P with n vertices and a point q∈P, we present an algorithm that reports the k-visibility region of q in P in O(cn/s+clog⁡s+min⁡{⌈k/s⌉n,nlog⁡logs⁡n}) expected time using O(s) words of workspace. Here, c∈{1,…,n} is the number of critical vertices of P for q where the k-visibility region of q may change. We generalize this result for polygons with holes and for sets of non-crossing line segments.

Space-efficient indexes for forbidden extension queries

Document listing is a fundamental problem in information retrieval. The objective is to retrieve all documents from a document collection that are relevant to an input pattern. Several variations of this problem such as ranked document retrieval, document listing with two patterns and forbidden patterns have been studied. We introduce the problem of document retrieval with forbidden extension. Let D={T1,T2,…,TD} be a collection of D string documents of n characters in total, and P+ and P− be two query patterns, where P+ is a proper prefix of P−. We call P− as the forbidden extension of the included pattern P+. A forbidden extension query 〈P+,P−〉 asks to report all occ documents in D that contains P+ as a substring, but does not contain P− as one. A top-k forbidden extension query 〈P+,P−,k〉 asks to report those k documents among the occ documents that are most relevant to P+, where each document is given a unique fixed score (PageRank) and the relevance of a document is determined based on its score. We present a linear index (in words) with an O(|P−|+occ) query time for the document listing problem. For the top-k version of the problem, we achieve the following space-time trade-offs:•O(n) space (in words) and O(|P−|log⁡σ+k) query time.•|CSA|+|CSA⁎|+Dlog⁡nD+O(n) bits and O(search(P−)+k⋅tSA⋅log2+ϵ⁡n) query time, where ϵ>0 is an arbitrarily small constant.•|CSA|+O(nlog⁡D) bits and O(search(P−)+(k+log⁡D)log⁡D) query time. Here σ is the size of the alphabet set, CSA (of size |CSA| bits) is the compressed suffix array (CSA) of the concatenated text of all documents, CSAd is the CSA of Td and |CSA⁎|=∑d=1D|CSAd|. Also, search(P−) is the time for pattern matching and tSA is the time to find suffix (or inverse suffix) array value.

Modelling Soil Water Content in a Tomato Field: Proximal Gamma Ray Spectroscopy and Soil–Crop System Models

Proximal soil sensors are taking hold in the understanding of soil hydrogeological processes involved in precision agriculture. In this context, permanently installed gamma ray spectroscopy stations represent one of the best space–time trade off methods at field scale. This study proved the feasibility and reliability of soil water content monitoring through a seven-month continuous acquisition of terrestrial gamma radiation in a tomato test field. By employing a 1 L sodium iodide detector placed at a height of 2.25 m, we investigated the gamma signal coming from an area having a ~25 m radius and from a depth of approximately 30 cm. Experimental values, inferred after a calibration measurement and corrected for the presence of biomass, were corroborated with gravimetric data acquired under different soil moisture conditions, giving an average absolute discrepancy of about 2%. A quantitative comparison was carried out with data simulated by AquaCrop, CRITeRIA, and IRRINET soil–crop system models. The different goodness of fit obtained in bare soil condition and during the vegetated period highlighted that CRITeRIA showed the best agreement with the experimental data over the entire data-taking period while, in presence of the tomato crop, IRRINET provided the best results.

A Time-Space Trade-off for the Shortest Path Tree in a Simple Polygon

A [Formula: see text]-workspace algorithm may use a workspace of [Formula: see text] words which can be read and written, in addition to their input, which is provided as a read-only array of [Formula: see text] items. We present a [Formula: see text]-workspace algorithm for constructing the shortest path tree of a simple polygon [Formula: see text] with [Formula: see text] vertices, with respect to a given point inside the polygon in [Formula: see text] time, where [Formula: see text] is the time for computing the visibility polygon of a given point inside a simple polygon with [Formula: see text] additional words of space.

Space-efficient algorithms for maximum cardinality search, its applications, and variants of BFS

Following the recent trends of designing space efficient algorithms for fundamental algorithmic graph problems, we present several time-space tradeoffs for performing maximum cardinality search (MCS), stack breadth first search, and queue breadth first search on a given input graph. As applications of these results, we also provide space-efficient implementations for testing if a given undirected graph is chordal, reporting an independent set, and a proper coloring of a given chordal graph among others. Finally, we also show how two other seemingly different graph problems and their algorithms have surprising connection with MCS with respect to designing space efficient algorithms.

Space Efficient Linear Time Algorithms for BFS, DFS and Applications

Research on space efficient graph algorithms, particularly for st-connectivity, has a long history including the celebrated polynomial time, O(lg n) bits1 algorithm in undirected graphs by Reingold J. JACM. 55(4) (2008), and polynomial time, \(n/2^{\Theta (\sqrt {\lg n})}\) bits algorithm in directed graphs by Barnes et al. SICOMP. 27(5), 1273–1282 (1998). Recent works by Asano et al. ISAAC (2014) and Elmasry et al. STACS (2015), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. Elmasry et al. gave, among others, an implementation of breadth first search (BFS) in a graph G with n vertices and m edges, taking the optimal O(m + n) time using O(n) bits improving the naive O(n lg n) bits implementation. Similarly, Asano et al. provided space efficient implementations for performing depth first search (DFS) in a graph G. We continue this line of work focusing on improving the space requirement for implementing a few classical graph algorithms. Our first result is a simple data structure that can maintain any subset S of a universe of u elements using just u + o(u) bits and supports in constant time, apart from the standard insert, delete and membership queries, the operation findany that finds and returns any element of the set (or outputs that the set is empty). It can also enumerate all elements present currently in the set in no particular order in O(k + 1) time where k is the number of elements currently belonging to the set. While this data structure supports a weaker set of operations than that of Elmasry et al. STACS (2015), it is simple, more space efficient and is sufficient to support a BFS implementation optimally in O(m + n) time using at most 2n + o(n) bits. Later, we further improve the space requirement of BFS to at most n lg 3 + o(n) bits albeit with a slight increase in running time to O(m lg nf(n)) time where f(n) is any extremely slow growing function of n, and the o term in the space is a function of f(n). We also discuss a similar time-space tradeoff result for finding a minimum weight spanning tree of a weighted (bounded by polynomial in n) undirected graph using n + O(n/f(n)) bits and O(m lg nf(n)) time, for any function f(n) such that 1 ≤ f(n) ≤ n. For DFS in a graph G, we provide an implementation taking O(m + n) time and O(n lg m/n) bits. This partially answers at least for sparse graphs, a question asked by Asano et al. ISAAC (2014) whether DFS can be performed in O (m + n) time and using O(n) bits, and also simultaneously improves the DFS result of Elmasry et al. STACS (2015). Using our DFS algorithm and other careful implementations, we show how one can also test for biconnectivity, 2-edge connectivity, and find cut vertices and bridges of a given undirected graph within the same time and space bounds; earlier classical linear time algorithms for these problems used Ω(n lg n) bits of space.

Approximate Polytope Membership Queries

In the polytope membership problem, a convex polytope $K$ in $\mathbb{R}^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given any query point $q \in \mathbb{R}^d$, it is possible to determine efficiently whether $q \in K$. We consider this problem in an approximate setting. Given an approximation parameter $\varepsilon$, the query can be answered either way if the distance from $q$ to $K$'s boundary is at most $\varepsilon$ times $K$'s diameter. We assume that the dimension $d$ is fixed, and $K$ is presented as the intersection of $n$ halfspaces. Previous solutions to approximate polytope membership were based on straightforward applications of classic polytope approximation techniques by Dudley (1974) and Bentley et al. (1982). The former is optimal in the worst-case with respect to space, and the latter is optimal with respect to query time. We present four main results. First, we show how to combine the two above techniques to obtain a simple space-time trade-off. Second, we present an algorithm that dramatically improves this trade-off. In particular, for any constant $\alpha \ge 4$, this data structure achieves query time $O(1/\varepsilon^{(d-1)/\alpha})$ and space roughly $O(1/\varepsilon^{(d-1)(1 - O(\log \alpha)/\alpha)})$. We do not know whether this space bound is tight, but our third result shows that there is a convex body such that our algorithm achieves a space of at least $\Omega( 1/\varepsilon^{(d-1)(1-O(\sqrt{\alpha})/\alpha} )$. Our fourth result shows that it is possible to reduce approximate Euclidean nearest neighbor searching to approximate polytope membership queries. Combined with the above results, this provides significant improvements to the best known space-time trade-offs for approximate nearest neighbor searching in $\mathbb{R}^d$.

Time–space trade-offs for Lempel–Ziv compressed indexing

Given a string S, the compressed indexing problem is to preprocess S into a compressed representation that supports fast substring queries. The goal is to use little space relative to the compressed size of S while supporting fast queries. We present a compressed index based on the Lempel–Ziv 1977 compression scheme. We obtain the following time–space trade-offs: For constant-sized alphabets(i)O(m+occlg⁡lg⁡n) time using O(zlg⁡(n/z)lg⁡lg⁡z) space, or(ii)O(m(1+lgϵ⁡zlg⁡(n/z))+occ(lg⁡lg⁡n+lgϵ⁡z)) time using O(zlg⁡(n/z)) space, For integer alphabets polynomially bounded by n(iii)O(m(1+lgϵ⁡zlg⁡(n/z))+occ(lg⁡lg⁡n+lgϵ⁡z)) time using O(z(lg⁡(n/z)+lg⁡lg⁡z)) space, or(iv)O(m+occ(lg⁡lg⁡n+lgϵ⁡z)) time using O(z(lg⁡(n/z)+lgϵ⁡z)) space, where n and m are the length of the input string and query string respectively, z is the number of phrases in the LZ77 parse of the input string, occ is the number of occurrences of the query in the input and ϵ>0 is an arbitrarily small constant. In particular, (i) improves the leading term in the query time of the previous best solution from O(mlg⁡m) to O(m) at the cost of increasing the space by a factor lg⁡lg⁡z. Alternatively, (ii) matches the previous best space bound, but has a leading term in the query time of O(m(1+lgϵ⁡zlg⁡(n/z))). However, for any polynomial compression ratio, i.e., z=O(n1−δ), for constant δ>0, this becomes O(m). Our index also supports extraction of any substring of length ℓ in O(ℓ+lg⁡(n/z)) time. Technically, our results are obtained by novel extensions and combinations of existing data structures of independent interest, including a new batched variant of weak prefix search.

Transfer Learning in Adaptive Filters: The Nearest Instance Centroid-Estimation Kernel Least-Mean-Square Algorithm

We propose a novel nearest-neighbors approach to organize and curb the growth of radial basis function network in kernel adaptive filtering (KAF). The nearest-instance-centroid-estimation (NICE) kernel least-mean-square (KLMS) algorithm provides an appropriate time-space tradeoff with good performance. Its centers in the input/feature space are organized by quasi-orthogonal regions for greatly simplified filter evaluation. Instead of using all centers to evaluate/update the function approximation at every new point, a linear search among the iteratively-updated centroids determines the partial function to be used, naturally forming locally-supported partial functionals. Under this framework, partial functionals that compose the adaptive filter are quickly stored/retrieved based on input, each corresponding to a specialized “spatial-band” subfilter. The filter evaluation becomes the update of one of the subfilters, creating a content addressable filter bank (CAFB). This CAFB is incrementally updated for new signal applications with mild constraints, always using the past-learned partial filter sums, opening the door for transfer learning and significant efficiency for new data scenarios, avoiding training from scratch as have been done since the invention of adaptive filtering. Using energy conservation relation, we show the sufficient condition for mean square convergence of the NICE-KLMS algorithm and establish the upper and lower bounds of steady-state excess-mean-square-error (EMSE). Simulations on chaotic time-series prediction demonstrate similar levels of accuracy as existing methods, but with much faster computation involving fewer input samples. Simulations on transfer learning using both synthetic and real-world data demonstrate that NICE CAFB can leverage previously learned knowledge to related task or domain.

Space–time trade-offs for finding shortest unique substrings and maximal unique matches

Given a string X[1,n] and a position k∈[1,n], a Shortest Unique Substring of X covering k, denoted by Sk, is a substring X[i,j] of X which satisfies the following conditions: (i)i≤k≤j, (ii)i is the only position where there is an occurrence of X[i,j], and (iii)j−i is minimized. Current best-known algorithms for finding Sk require Θ(n) words of working space, and O(n) time. Let τ be a given parameter. We present the following new results.•Given a k∈[1,n], we can compute Sk in O(nτ2log⁡nτ) time using X and an additional O(n/τ) words of working space.•For every k∈[1,n], we can compute Sk in O(nτ2log⁡n) time using X, and an additional O(n/τ) words and 4n+o(n) bits of working space.•We present an O(nτlogc+1⁡n)-time randomized algorithm that uses n/logc⁡n words in addition to that mentioned above, where c≥0 is an arbitrary constant. In this case, the reported string is unique and covers k, but, with probability at most n−O(1), may not be the shortest.By choosing τ=ω(1), our results imply the first sub-linear space (in addition to the input string) solution to these problems. We also present the following two results.•An algorithm that finds Sk for every k∈[1,n] using O(nlog⁡σ) bits of working space in O(nlog⁡n) time, where σ≤n is the number of distinct symbols in X.•A 4n+o(n)-bit index that can report Sk for any k in O(1) time. As a consequence of our techniques, we also obtain similar space-and-time tradeoffs for a related problem of finding Maximal Unique Matches of two strings (Delcher et al., 1999 [14]).

Horizontally scalable probabilistic generalized suffix tree (PGST) based route prediction using map data and GPS traces

Route prediction is an essential requirement for many intelligent transport systems (ITS) services like VANETS, traffic congestion estimation, resource prediction in grid computing etc. This work focuses on building an end-to-end horizontally scalable route prediction application based on statistical modeling of user travel data. Probabilistic suffix tree (PST) is one of widely used sequence indexing technique which serves a model for prediction. The probabilistic generalized suffix tree (PGST) is a variant of PST and is essentially a suffix tree built from a huge number of smaller sequences. We construct generalized suffix tree model from a large number of trips completed by the users. User trip raw GPS traces is mapped to the digitized road network by parallelizing map matching technique leveraging map reduce framework. PGST construction from the huge volume of data by processing sequentially is a bottleneck in the practical realization. Most of the existing works focused on time-space tradeoffs on a single machine. Proposed technique solves this problem by a two-step process which is intuitive to execute in the map-reduce framework. In the first step, computes all the suffixes along with their frequency of occurrences and in the second step, builds probabilistic generalized suffix tree. The probabilistic aspect of the tree is also taken care so that it can be used as a model for prediction application. Dataset used are road network spatial data and GPS traces of users. Experiments carried out on real datasets available in public domain.

Quantum algorithm to solve function inversion with time–space trade-off

In general, it is a difficult problem to solve the inverse of any function. With the inverse implication operation, we present a quantum algorithm for solving the inversion of function via using time---space trade-off in this paper. The details are as follows. Let function $$f(x)=y$$f(x)=y have k solutions, where $$x\in \{0, 1\}^{n}, y\in \{0, 1\}^{m}$$x?{0,1}n,y?{0,1}m for any integers n, m. We show that an iterative algorithm can be used to solve the inverse of function f(x) with successful probability $$1-\left( 1-\frac{k}{2^{n}}\right) ^{L}$$1-1-k2nL for $$L\in Z^{+}$$L?Z+. The space complexity of proposed quantum iterative algorithm is O(Ln), where L is the number of iterations. The paper concludes that, via using time---space trade-off strategy, we improve the successful probability of algorithm.

Equihash: Asymmetric Proof-of-Work Based on the Generalized Birthday Problem

Proof-of-work is a central concept in modern cryptocurrencies and denial-ofservice protection tools, but the requirement for fast verification so far has made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on memory-intensive computations in order to remedy the disparity between architectures have resulted in slow or broken schemes. In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW) based on a computationally-hard problem, which requires a great deal of memory to generate a proof (called a ”memory-hardness” feature) but is instant to verify. Our primary proposal, Equihash, is a PoW based on the generalized birthday problem and enhanced Wagner’s algorithm for it. We introduce the new technique of algorithm binding to prevent cost amortization and demonstrate that possible parallel implementations are constrained by memory bandwidth. Our scheme has tunable and steep time-space tradeoffs, which impose large computational penalties if less memory is used. Our solution is practical and ready to deploy: a reference implementation of a proof-of-work requiring 700 MB of RAM runs in 15 seconds on a 2.1 GHz CPU, increases the computations by a factor of 1000 if memory is halved, and presents a proof of just 120 bytes long.

Semi-Group Range Sum Revisited: Query-Space Lower Bound Tightened

Let $$\mathcal {D}$$ be a set of n elements $$e_1,\ldots , e_n$$ drawn from a commutative semigroup. Given two integers x, y satisfying $$1 \le x \le y \le n$$ , a range sum query returns the sum of the $$y-x+1$$ elements $$e_x$$ , $$e_{x+1}$$ ,..., $$e_y$$ . The goal of indexing is to store $$\mathcal {D}$$ in a data structure so that all such queries can be answered efficiently in the worst case. This paper proves a new lower bound in the semigroup model on the tradeoff between space and query time for the above problem. We show that, if the query time needs to be at most an integer t, a structure must use space. The bound is asymptotically tight for every $$t \ge 2$$ , and is matched by an existing structure. Previously, the best lower bounds either had a substantially smaller non-linear factor (Yao in Space-time tradeoff for answering range queries (extended abstract). In: STOC, pp. 128–136, 1982), or were tight only for constant t (Alon and Schieber in Optimal preprocessing for answering on-line product queries. Technical Report TR 71/87, Tel-Aviv University, 1987). Our lower bound is asymptotically tight bidirectionally, namely, it also answers the following question: if the space needs to be bounded by an integer m, what is the best query time achievable? The techniques behind our lower bound are drastically different from those of Yao (Space-time tradeoff for answering range queries (extended abstract). In: STOC, pp. 128–136, 1982) and Alon and Schieber (Optimal preprocessing for answering on-line product queries. Technical Report TR 71/87, Tel-Aviv University, 1987), and reveal new insight on the characteristics of the problem.

Dictionary Matching with a Bounded Gap in Pattern or in Text

A gap is a sequence of don’t care characters. In this paper, we study two variants of the dictionary matching problem, where gaps may be present in the patterns or in the text. The first variant, called dictionary matching with one gap, considers indexing a collection \({\mathcal D}\) of d one-gap-patterns, where the ith pattern is of the form \(P_i[\alpha _i,\beta _i]Q_i\) with \(P_i\) and \(Q_i\) are strings drawn from an alphabet \(\varSigma \) and \([\alpha _i, \beta _i]\) denote the lower and upper bounds on the gap length. The target is to allow a user to efficiently identify all substrings of a query text T that match with any one-gap-pattern in the collection. We present a linear space solution for answering the above dictionary matching query in time \(O(|T| \gamma \log \lambda \log d+\mathsf {occ})\), where \(\gamma \) denotes the number of distinct gap lengths, \(\lambda \) denotes the number of distinct lower and upper bounds of gap lengths, and the \(\mathsf {occ}\) is the output size. The query time can be improved to \(O(|T|\gamma +\mathsf {occ})\) using \(O(d^{1+\epsilon })\) extra space, where \(\epsilon >0\) is an arbitrarily small constant. Additionally, we show a succinct-space index offering a space–time tradeoff. In the special case where parameters \(\alpha _i\) and \(\beta _i\)’s for all the patterns are same, our results improve upon the work by Amir et al. (Proceedings of annual symposium on combinatorial pattern matching (CPM), 2014, Theor Comput Sci 589:34–46, 2015). The second variant, called dictionary matching with one missing substring, is a new problem in which a gap of bounded length may be present in the text substring when it is being matched. We show that this problem can be solved by using a similar framework. Furthermore, by applying a centroid path decomposition on the failure tree, we obtain a space–time tradeoff result, which will be suitable when the dictionary contains only short patterns, or when index space is a critical concern.

POSTER

It's important to hit a space-time balance for a real-world algorithm to achieve high performance on modern shared-memory multi-core or many-core systems. However, a large class of dynamic programs with more than $O(1)$ dependency achieve optimality either in space or time, but not both. In the literature, the problem is known as the fundamental space-time tradeoff. By exploiting properly on the runtime system, we show that our STAR (Space-Time Adaptive and Reductive) technique can help these dynamic programs to achieve sublinear parallel time bounds while still maintaining work-, space-, and cache-optimality in a processor- and cache-oblivious fashion.

Time–space trade-offs for triangulations and Voronoi diagrams

Let S be a planar n-point set. A triangulation for S is a maximal plane straight-line graph with vertex set S. The Voronoi diagram for S is the subdivision of the plane into cells such that all points in a cell have the same nearest neighbor in S. Classically, both structures can be computed in O(nlog⁡n) time and O(n) space. We study the situation when the available workspace is limited: given a parameter s∈{1,…,n}, an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of Θ(log⁡n) bits for reading and writing intermediate data. The output should then be written to a write-only structure. We describe a deterministic s-workspace algorithm for computing an arbitrary triangulation of S in time O(n2/s+nlog⁡nlog⁡s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s)log⁡s+nlog⁡slog⁎⁡s).

A Practical Index for Approximate Dictionary Matching with Few Mismatches

Approximate dictionary matching (checking if a pattern occurs in a collection of strings) is a classic problem with applications in e.g. spellchecking, online catalogs, and web searchers. We present a simple solution called split index, which is based on the Dirichlet principle, for matching a keyword with few mismatches, and experimentally show that it offers competitive space-time tradeoffs. Our implementation in the C++ language is focused mostly on data compaction, which is beneficial for the search speed. We compare our solution with other algorithms and we show that it is faster when the Hamming distance is used. Query times in the order of 1 microsecond were reported for one mismatch for a few-megabyte natural language dictionary on a medium-end PC. We also demonstrate that a basic compression technique consisting in q-gram substitution can significantly reduce the index size (up to 50 % of the input text size for the DNA sequences).

Hashedcubes: Simple, Low Memory, Real-Time Visual Exploration of Big Data.

We propose Hashedcubes, a data structure that enables real-time visual exploration of large datasets that improves the state of the art by virtue of its low memory requirements, low query latencies, and implementation simplicity. In some instances, Hashedcubes notably requires two orders of magnitude less space than recent data cube visualization proposals. In this paper, we describe the algorithms to build and query Hashedcubes, and how it can drive well-known interactive visualizations such as binned scatterplots, linked histograms and heatmaps. We report memory usage, build time and query latencies for a variety of synthetic and real-world datasets, and find that although sometimes Hashedcubes offers slightly slower querying times to the state of the art, the typical query is answered fast enough to easily sustain a interaction. In datasets with hundreds of millions of elements, only about 2% of the queries take longer than 40ms. Finally, we discuss the limitations of data structure, potential spacetime tradeoffs, and future research directions.

Prioritized garbage collection: explicit GC support for software caches

Programmers routinely trade space for time to increase performance, often in the form of caching or memoization. In managed languages like Java or JavaScript, however, this space-time tradeoff is complex. Using more space translates into higher garbage collection costs, especially at the limit of available memory. Existing runtime systems provide limited support for space-sensitive algorithms, forcing programmers into difficult and often brittle choices about provisioning. This paper presents prioritized garbage collection , a cooperative programming language and runtime solution to this problem. Prioritized GC provides an interface similar to soft references, called priority references , which identify objects that the collector can reclaim eagerly if necessary. The key difference is an API for defining the policy that governs when priority references are cleared and in what order. Application code specifies a priority value for each reference and a target memory bound. The collector reclaims references, lowest priority first, until the total memory footprint of the cache fits within the bound. We use this API to implement a space-aware least-recently-used (LRU) cache, called a Sache , that is a drop-in replacement for existing caches, such as Google's Guava library. The garbage collector automatically grows and shrinks the Sache in response to available memory and workload with minimal provisioning information from the programmer. Using a Sache, it is almost impossible for an application to experience a memory leak, memory pressure, or an out-of-memory crash caused by software caching.