Related papers: Subtree Mode and Applications
The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting)…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the…
Color-constrained subgraph problems are those where we are given an edge-colored (directed or undirected) graph and the task is to find a specific type of subgraph, like a spanning tree, an arborescence, a single-source shortest path tree,…
In a vertex-colored graph $G = (V, E)$, a subset $S \subseteq V$ is said to be consistent if every vertex has a nearest neighbor in $S$ with the same color. The problem of computing a minimum cardinality consistent subset of a graph is…
Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to find all the $k$-vertex subgraphs that appear with frequency greater than a given threshold. FSM has numerous applications ranging from biology to network science, as…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
Let $R$ and $B$ be two disjoint sets of points in the plane where the points of $R$ are colored red and the points of $B$ are colored blue, and let $n=|R\cup B|$. A bichromatic spanning tree is a spanning tree in the complete bipartite…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
In this paper we describe a new efficient (in fact optimal) data structure for the {\em top-$K$ color problem}. Each element of an array $A$ is assigned a color $c$ with priority $p(c)$. For a query range $[a,b]$ and a value $K$, we have to…
We consider the range mode problem where given a sequence and a query range in it, we want to find items with maximum frequency in the range. We give time- and space- efficient algorithms for this problem. Our algorithms are efficient for…
We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to select the modes relevant for reduction are usually…
The Minimum Consistent Subset (MCS) problem arises naturally in the context of supervised clustering and instance selection. In supervised clustering, one aims to infer a meaningful partitioning of data using a small labeled subset.…
A rooted tree $\vec{R}$ is a rooted subtree of a tree $T$ if the tree obtained by replacing the directed edges of $\vec{R}$ by undirected edges is a subtree of $T$. We study the problem of assigning minimum number of colors to a given set…
In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$…
This thesis tackles the problem of learning efficient representations of complex, structured data with a natural application to web page and element classification. We hypothesise that the context around the element inside the web page is…
We introduce an efficient method for training the linear ranking support vector machine. The method combines cutting plane optimization with red-black tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time complexity,…
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open…