Searcharxiv⌕ Search

arXiv subjects

Enoch Peserico

Publications and source records attributed to Enoch Peserico.

10 recordsLinked to original sources
arXiv2026

Is competitive online paging an artifact?

In any real system a newly computed datum begins its existence in the processor rather than in external memory, and thus does not inevitably incur a cold miss. This was captured by early I/O models, but not by the Sleator-Tarjan one that has come to underpin competitive analysis of paging. If one corrects the Sleator-Tarjan model by charging no cost for the first access to newly computed data, optimal offline algorithms such as LFD remain optimal, but no online paging algorithm can be competitive, even if randomized, even with arbitrary resource augmentation, even against request sequences that are not tailored against it but are instead representative of widely used computational techniques. The proofs are simple, and appear robust against any reasonable assumption/model adjustment, including virtually all tools developed to make competitive analysis less pessimistic. In other words, while competitive analysis does predict the good performance exhibited in practice by online paging algorithms such as LRU, these predictions seem just a fortuitous artifact of an incorrect assumption that has crept into the underlying model several decades ago. And there are implications beyond paging, too: for example, the same issue undermines the Ideal Cache model on which the popular Cache-Oblivious and Cache-Adaptive algorithmic frameworks are based.

cs.DS↗
arXiv2018

Sublinear algorithms for local graph centrality estimation

We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of elementary operations. We develop a technique, that we apply to the PageRank and Heat Kernel centralities, for building a low-variance score estimator through a local exploration of the graph. We obtain an algorithm that, given any node in any graph of $m$ arcs, with probability $(1-δ)$ computes a multiplicative $(1\pmε)$-approximation of its score by examining only $\tilde{O}(\min(m^{2/3} Δ^{1/3} d^{-2/3},\, m^{4/5} d^{-3/5}))$ nodes/arcs, where $Δ$ and $d$ are respectively the maximum and average outdegree of the graph (omitting for readability $\operatorname{poly}(ε^{-1})$ and $\operatorname{polylog}(δ^{-1})$ factors). A similar bound holds for computational complexity. We also prove a lower bound of $Ω(\min(m^{1/2} Δ^{1/2} d^{-1/2}, \, m^{2/3} d^{-1/3}))$ for both query complexity and computational complexity. Moreover, our technique yields a $\tilde{O}(n^{2/3})$ query complexity algorithm for the graph access model of [Brautbar et al., 2010], widely used in social network mining; we show this algorithm is optimal up to a sublogarithmic factor. These are the first algorithms yielding worst-case sublinear bounds for general directed graphs and any choice of the target node.

cs.DS↗
arXiv2018

Deterministic oblivious distribution (and tight compaction) in linear time

In an array of N elements, M positions and M elements are "marked". We show how to permute the elements in the array so that all marked elements end in marked positions, in time O(N) (in the standard word-RAM model), deterministically, and obliviously - i.e. with a sequence of memory accesses that depends only on N and not on which elements or positions are marked. As a corollary, we answer affirmatively to an open question about the existence of a deterministic oblivious algorithm with O(N) running time for tight compaction (move the M marked elements to the first M positions of the array), a building block for several cryptographic constructions. Our O(N) result improves the running-time upper bounds for deterministic tight compaction, for randomized tight compaction, and for the simpler problem of randomized loose compaction (move the M marked elements to the first O(M) positions) - until now respectively O(N lg N), O(N lg lg N), and O(N lg*N).

cs.DS↗
arXiv2018

Simple set cardinality estimation through random sampling

We present a simple algorithm that estimates the cardinality $n$ of a set $V$ when allowed to sample elements of $V$ uniformly and independently at random. Our algorithm with probability $(1-δ)$ returns a $(1\pmε)-$approximation of $n$ drawing $O\big(\sqrt{n} \cdot ε^{-1}\sqrt{\log(δ^{-1})}\big)$ samples (for $ε^{-1}\sqrt{\log(δ^{-1})} = O(\sqrt{n})$).

cs.DM↗
arXiv2017

On approximating the stationary distribution of time-reversible Markov chains

Approximating the stationary probability of a state in a Markov chain through Markov chain Monte Carlo techniques is, in general, inefficient. Standard random walk approaches require $\tilde{O}(τ/π(v))$ operations to approximate the probability $π(v)$ of a state $v$ in a chain with mixing time $τ$, and even the best available techniques still have complexity $\tilde{O}(τ^{1.5}/π(v)^{0.5})$, and since these complexities depend inversely on $π(v)$, they can grow beyond any bound in the size of the chain or in its mixing time. In this paper we show that, for time-reversible Markov chains, there exists a simple randomized approximation algorithm that breaks this "small-$π(v)$ barrier".

cs.DM↗
arXiv2016

Community structure and interaction dynamics through the lens of quotes

This is the first work investigating community structure and interaction dynamics through the lens of quotes in online discussion forums. We examine four forums of different size, language, and topic. Quote usage, which is surprisingly consistent over time and users, appears to have an important role in aiding intra-thread navigation, and uncovers a hidden "social" structure in communities otherwise lacking all trappings (from friends and followers to reputations) of today's social networks.

cs.SI↗
arXiv2016

The Power of Local Information in PageRank

How large a fraction of a graph must one explore to rank a small set of nodes according to their PageRank scores? We show that the answer is quite nuanced, and depends crucially on the interplay between the correctness guarantees one requires and the way one can access the graph. On the one hand, assuming the graph can be accessed only via "natural" exploration queries that reveal small pieces of its topology, we prove that deterministic and Las Vegas algorithms must in the worst case perform $n - o(n)$ queries and explore essentially the entire graph, independently of the specific types of query employed. On the other hand we show that, depending on the types of query available, Monte Carlo algorithms can perform asymptotically better: if allowed to both explore the local topology around single nodes and access nodes at random in the graph they need $Ω(n^{2/3})$ queries in the worst case, otherwise they still need $Ω(n)$ queries similarly to Las Vegas algorithms. All our bounds generalize and tighten those already known, cover the different types of graph exploration queries appearing in the literature, and immediately apply also to the problem of approximating the PageRank score of single nodes.

cs.DM↗
arXiv2013

Paging with dynamic memory capacity

We study a generalization of the classic paging problem that allows the amount of available memory to vary over time - capturing a fundamental property of many modern computing realities, from cloud computing to multi-core and energy-optimized processors. It turns out that good performance in the "classic" case provides no performance guarantees when memory capacity fluctuates: roughly speaking, moving from static to dynamic capacity can mean the difference between optimality within a factor 2 in space and time, and suboptimality by an arbitrarily large factor. More precisely, adopting the competitive analysis framework, we show that some online paging algorithms, despite having an optimal (h,k)-competitive ratio when capacity remains constant, are not (3,k)-competitive for any arbitrarily large k in the presence of minimal capacity fluctuations. In this light it is surprising that several classic paging algorithms perform remarkably well even if memory capacity changes adversarially - even without taking those changes into explicit account! In particular, we prove that LFD still achieves the minimum number of faults, and that several classic online algorithms such as LRU have a "dynamic" (h,k)-competitive ratio that is the best one can achieve without knowledge of future page requests, even if one had perfect knowledge of future capacity fluctuations (an exact characterization of this ratio shows it is almost, albeit not quite, equal to the "classic" ratio k/(k-h+1)). In other words, with careful management, knowing/predicting future memory resources appears far less crucial to performance than knowing/predicting future data accesses.

cs.DS↗
arXiv2008

The rank convergence of HITS can be slow

We prove that HITS, to "get right" h of the top k ranked nodes of an N>=2k node graph, can require h^(Omega(N h/k)) iterations (i.e. a substantial Omega(N h log(h)/k) matrix multiplications even with a "squaring trick"). Our proof requires no algebraic tools and is entirely self-contained.

cs.DS↗