Related papers: Indexing Graph Search Trees and Applications
The focus of this paper is two fold. Firstly, we present a logical approach to graph modification problems such as minimum node deletion, edge deletion, edge augmentation problems by expressing them as an expression in first order (FO)…
We present a new fast all-pairs shortest path algorithm for unweighted graphs. In breadth-first search which is said to representative and fast in unweighted graphs, the average number of accesses to adjacent vertices (expressed by…
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 graph G and a query vertex q, the topic of community search (CS), aiming to retrieve a dense subgraph of G containing q, has gained much attention. Most existing works focus on undirected graphs which overlooks the rich information…
We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially $n$ nodes and O(n) edges and monotone update sequences of either $\Theta(n)$ edge insertions…
The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large…
This note recapitulates an algorithmic observation for ordered Depth-First Search (DFS) in directed graphs that immediately leads to a parallel algorithm with linear speed-up for a range of processors for non-sparse graphs. The note extends…
We combine two methods for the lossless compression of unlabeled graphs - entropy compressing adjacency lists and computing canonical names for vertices - and solve an ensuing novel optimisation problem: Minimum-Entropy Tree-Extraction…
We consider $m \times s$ matrices (with $m\geq s$) in a real affine subspace of dimension $n$. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
Large Language Models (LLMs) have demonstrated remarkable improvements in reasoning and planning through increased test-time compute, often by framing problem-solving as a search process. While methods like Monte Carlo Tree Search (MCTS)…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
The suffix array is an efficient data structure for in-memory pattern search. Suffix arrays can also be used for external-memory pattern search, via two-level structures that use an internal index to identify the correct block of suffix…
We define and study analogs of probabilistic tree embedding and tree cover for directed graphs. We define the notion of a DAG cover of a general directed graph $G$: a small collection $D_1,\dots D_g$ of DAGs so that for all pairs of…
The treedepth of a graph $G$ is the least possible depth of an elimination forest of $G$: a rooted forest on the same vertex set where every pair of vertices adjacent in $G$ is bound by the ancestor/descendant relation. We propose an…
Graph searching is one of the simplest and most widely used tools in graph algorithms. Every graph search method is defined using some particular selection rule, and the analysis of the corresponding vertex orderings can aid greatly in…
Natural language text corpora are often available as sets of syntactically parsed trees. A wide range of expressive tree queries are possible over such parsed trees that open a new avenue in searching over natural language text. They not…
Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved that…
Graph plays a vital role in representing entities and their relationships in a variety of fields, such as e-commerce networks, social networks and biological networks. Given two vertices s and t, one of the fundamental problems in graph…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…