Related papers: Optimal Prefix Free Codes With Partial Sorting

An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…

We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting $n$ distinct elements in this model. In particular, it…

We consider the problem of encoding a string of length $n$ from an integer alphabet of size $\sigma$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any…

Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…

In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…

Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling,…

Given a probability distribution over a set of n words to be transmitted, the Huffman Coding problem is to find a minimal-cost prefix free code for transmitting those words. The basic Huffman coding problem can be solved in O(n log n) time…

A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…

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…

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the $[\Theta(\log n), \Theta(n)]$ region, in two settings. We present one…

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g.,…

The integer complexity $f(n)$ of a positive integer $n$ is defined as the minimum number of 1's needed to represent $n$, using additions, multiplications and parentheses. We present two simple and faster algorithms for computing the integer…

We show how to build an alphabetic minimax tree for a sequence (W = w_1, >..., w_n) of real weights in (O (n d \log \log n)) time, where $d$ is the number of distinct integers (\lceil w_i \rceil). We apply this algorithm to building an…

Roughly speaking, an $(n,(r,s))$-Cover Free Family (CFF) is a small set of $n$-bit strings such that: "in any $d:=r+s$ indices we see all patterns of weight $r$". CFFs have been of interest for a long time both in discrete mathematics as…

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

In this paper we study the problem of sorting under non-uniform comparison costs, where costs are either 1 or $\infty$. If comparing a pair has an associated cost of $\infty$ then we say that such a pair cannot be compared (forbidden…

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…

We present the first explicit comparison-based algorithm that sorts the sumset $X + Y = \{x_i + y_j,\ \forall 0 \le i, j < n\}$, where $X$ and $Y$ are sorted arrays of real numbers, in optimal $O(n^2)$ time and comparisons. While Fredman…

A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. Variants of this problem have seen…

We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…