Related papers: Hardness of Regular Expression Matching with Exten…
Given $d$ strings over the alphabet $\{0,1,\ldots,\sigma{-}1\}$, the classical Aho--Corasick data structure allows us to find all $occ$ occurrences of the strings in any text $T$ in $O(|T| + occ)$ time using $O(m\log m)$ bits of space,…
Detecting if a graph contains a $k$-Clique is one of the most fundamental problems in computer science. The asymptotically fastest algorithm runs in time $O(n^{\omega k/3})$, where $\omega$ is the exponent of Boolean matrix multiplication.…
In the $(k,m)$-mappability problem, for a given sequence $T$ of length $n$, the goal is to compute a table whose $i$th entry is the number of indices $j \ne i$ such that the length-$m$ substrings of $T$ starting at positions $i$ and $j$…
Let $P$ be a set of $2n$ points in the plane, and let $M_{\rm C}$ (resp., $M_{\rm NC}$) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of $P$. We study the problem of computing $M_{\rm NC}$. We first prove that the…
We consider the problem of preprocessing an $n\times n$ matrix $\mathbf{M}$, and supporting queries that, for any vector $v$, returns the matrix-vector product $\mathbf{M} v$. This problem has been extensively studied in both theory and…
Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…
Given a pattern string $P$ of length $n$ consisting of $\delta$ distinct characters and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet $\Sigma$ of size $\Delta$, the {\em exact string…
Template matching is widely used for many applications in image and signal processing and usually is time-critical. Traditional methods usually focus on how to reduce the search locations by coarse-to-fine strategy or full search combined…
Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these…
Given two positions $i$ and $j$ in a string $T$ of length $N$, a longest common extension (LCE) query asks for the length of the longest common prefix between suffixes beginning at $i$ and $j$. A compressed LCE data structure is a data…
Given two sets $S$ and $T$ of points in the plane, of total size $n$, a {many-to-many} matching between $S$ and $T$ is a set of pairs $(p,q)$ such that $p\in S$, $q\in T$ and for each $r\in S\cup T$, $r$ appears in at least one such pair.…
We first show that the Traveling Salesman Problem in an n-vertex graph with average degree bounded by d can be solved in O*(2^{(1-\eps_d)n}) time and exponential space for a constant \eps_d depending only on d, where the O*-notation…
In the fundamental Maximum Matching problem the task is to find a maximum cardinality set of pairwise disjoint edges in a given undirected graph. The fastest algorithm for this problem, due to Micali and Vazirani, runs in time…
The extension complexity of a polytope $P$ is the smallest integer $k$ such that $P$ is the projection of a polytope $Q$ with $k$ facets. We study the extension complexity of $n$-gons in the plane. First, we give a new proof that the…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
In this paper, we investigate the model checking (MC) problem for Halpern and Shoham's interval temporal logic HS. In the last years, interval temporal logic MC has received an increasing attention as a viable alternative to the traditional…
We study the problem of estimating the size of maximum matching and minimum vertex cover in sublinear time. Denoting the number of vertices by $n$ and the average degree in the graph by $\bar{d}$, we obtain the following results for both…
The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…
In many applications, it is necessary to determine the string similarity. Edit distance[WF74] approach is a classic method to determine Field Similarity. A well known dynamic programming algorithm [GUS97] is used to calculate edit distance…
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class…