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In the Dictionary-based String Matching (DSM) problem, a retrieval system has access to a source sequence and stores the position of a certain number of strings in a posting table. When a user inquires the position of a string, the…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
We consider the problem of matching a metric space $(X,d_X)$ of size $k$ with a subspace of a metric space $(Y,d_Y)$ of size $n \geq k$, assuming that these two spaces have constant doubling dimension $\delta$. More precisely, given an…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…
Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees.…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
The order preserving pattern matching (OPPM) problem is, given a pattern string $p$ and a text string $t$, find all substrings of $t$ which have the same relative orders as $p$. In this paper, we consider two variants of the OPPM problem…
In rectangle packing problems we are given the task of placing axis-aligned rectangles in a given plane region, so that they do not overlap with each other. In Maximum Weight Independent Set of Rectangles (MWISR), their position is given…
In this paper, we consider a generalized longest common subsequence problem with multiple substring inclusive constraints. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints $P=\{P_1,\cdots,P_d\}$…
In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
Let $T$ be a tree space (or tree network) represented by a weighted tree with $t$ vertices, and $S$ be a set of $n$ stochastic points in $T$, each of which has a fixed location with an independent existence probability. We investigate two…
For a required payload, the existing reversible data hiding (RDH) methods always expect to reduce the embedding distortion as much as possible, such as by utilizing a well-designed predictor, taking into account the carrier-content…
Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from…
The coverage depth problem in DNA data storage is about computing the expected number of reads needed to recover all encoded strands. Given a generator matrix of a linear code, this quantity equals the expected number of randomly drawn…
Deep semantic matching aims to discriminate the relationship between documents based on deep neural networks. In recent years, it becomes increasingly popular to organize documents with a graph structure, then leverage both the intrinsic…
This paper introduces the \emph{$d$-distance $b$-matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges, an integer $d\in\mathbb{Z}_+$ and a degree bound function…
Problems with solutions represented by permutations are very prominent in combinatorial optimization. Thus, in recent decades, a number of evolutionary algorithms have been proposed to solve them, and among them, those based on probability…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…