Related papers: An Optimal Choice Dictionary
A key principle in string processing is local consistency: using short contexts to handle matching fragments of a string consistently. String synchronizing sets [Kempa, Kociumaka; STOC 2019] are an influential instantiation of this…
Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…
We develop dynamic dictionaries on the word RAM that use asymptotically optimal space, up to constant factors, subject to insertions and deletions, and subject to supporting perfect-hashing queries and/or membership queries, each operation…
We suggest a method for holding a dictionary data structure, which maps keys to values, in the spirit of Bloom Filters. The space requirements of the dictionary we suggest are much smaller than those of a hashtable. We allow storing n keys,…
We present a data structure representing a dynamic set S of w-bit integers on a w-bit word RAM. With |S|=n and w > log n and space O(n), we support the following standard operations in O(log n / log w) time: - insert(x) sets S = S + {x}. -…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the…
A rank-select index for a sequence $B=(b_1,\ldots,b_n)$ of $n$ bits is a data structure that, if provided with an operation to access $\Theta(\log n)$ arbitrary consecutive bits of $B$ in constant time (thus $B$ is stored outside of the…
In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\texttt{fill}(\Delta)$ operation which sets every entry of to some $\Delta\in\{0,\ldots,2^w-1\}$. We…
We show how to construct a dynamic ordered dictionary, supporting insert/delete/rank/select on a set of $n$ elements from a universe of size $U$, that achieves the optimal amortized expected time complexity of $O(1 + \log n / \log \log U)$,…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
Let $A$ be a static array storing $n$ elements from a totally ordered set. We present a data structure of optimal size at most $n\log_2(3+2\sqrt{2})+o(n)$ bits that allows us to answer the following queries on $A$ in constant time, without…
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms…
The observed frequency of the longest proper prefix, the longest proper suffix, and the longest infix of a word $w$ in a given sequence $x$ can be used for classifying $w$ as avoided or overabundant. The definitions used for the expectation…
Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…
This paper introduces a new data-structural object that we call the tiny pointer. In many applications, traditional $\log n $-bit pointers can be replaced with $o (\log n )$-bit tiny pointers at the cost of only a constant-factor time…
A Random Access query to a string $T\in [0..\sigma)^n$ asks for the character $T[i]$ at a given position $i\in [0..n)$. In $O(n\log\sigma)$ bits of space, this fundamental task admits constant-time queries. While this is optimal in the…
An agent who lacks preferences and instead makes decisions using criteria that are costly to create should select efficient sets of criteria, where the cost of making a given number of choice distinctions is minimized. Under mild…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…