Related papers: Optimal Non-Adaptive Cell Probe Dictionaries and H…
Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal…
We consider the dynamic dictionary problem for multisets. Given an upper bound $n$ on the total cardinality of the multiset (i.e., including multiplicities) at any point in time, the goal is to design a data structure that supports…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
Several novel frameworks for hyperparameter search have emerged in the last decade, but most rely on strict, often normal, distributional assumptions, limiting search model flexibility. This paper proposes a novel optimization framework…
Hashing technology has been widely used in image retrieval due to its computational and storage efficiency. Recently, deep unsupervised hashing methods have attracted increasing attention due to the high cost of human annotations in the…
Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…
Keyword search in relational databases has been widely studied in recent years because it does not require users neither to master a certain structured query language nor to know the complex underlying database schemas. Most of existing…
We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are…
Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…
This paper presents a logic language for expressing NP search and optimization problems. Specifically, first a language obtained by extending (positive) Datalog with intuitive and efficient constructs (namely, stratified negation,…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus…
We consider the problem of proper learning a Boolean Halfspace with integer weights $\{0,1,\ldots,t\}$ from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks $n^{O(t^5)}$ membership…
A key part of implementing high-level languages is providing built-in and default data structures. Yet selecting good defaults is hard. A mutable data structure's workload is not known in advance, and it may shift over its lifetime - e.g.,…
We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of $d$ strings of length $m$ and an integer $k$, we must preprocess it into a data structure to answer the following queries: Given a query…
In the era of big data, methods for improving memory and computational efficiency have become crucial for successful deployment of technologies. Hashing is one of the most effective approaches to deal with computational limitations that…
Tries are popular data structures for storing a set of strings, where common prefixes are represented by common root-to-node paths. Over fifty years of usage have produced many variants and implementations to overcome some of their…
We provide a static data structure for distance estimation which supports {\it adaptive} queries. Concretely, given a dataset $X = \{x_i\}_{i = 1}^n$ of $n$ points in $\mathbb{R}^d$ and $0 < p \leq 2$, we construct a randomized data…