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Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. We continue this line of work focusing on space. Our first result is a…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
Breadth-First Search (BFS) is a fundamental graph kernel that underpins a wide range of applications. While modern GPUs provide specialised Matrix-Multiply-Accumulate (MMA) units, e.g., Tensor Cores (TC), with extremely high throughput,…
Greedy best-first search (GBFS) and A* search (A*) are popular algorithms for path-finding on large graphs. Both use so-called heuristic functions, which estimate how close a vertex is to the goal. While heuristic functions have been…
Graph processing at scale presents many challenges, including the irregular structure of graphs, the latency-bound nature of graph algorithms, and the overhead associated with distributed execution. While existing frameworks such as Spark…
A feature selection algorithm should ideally satisfy four conditions: reliably extract relevant features; be able to identify non-linear feature interactions; scale linearly with the number of features and dimensions; allow the…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
Graph-based approximate nearest neighbor search has attracted more and more attentions due to its online search advantages. Numbers of methods studying the enhancement of speed and recall have been put forward. However, few of them focus on…
Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…
Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the…
It is now well-admitted that formal methods are helpful for many issues raised in the Web service area. In this paper we present a framework for the design and verification of WSs using process algebras and their tools. We define a two-way…
A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…
Matrix/array analysis of networks can provide significant insight into their behavior and aid in their operation and protection. Prior work has demonstrated the analytic, performance, and compression capabilities of GraphBLAS…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
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…
Full stack software applications are often simplified to basic CRUD operations, which can overlook the intricate principles of computer science necessary for addressing complex development challenges. Current methodologies frequently fall…
In this paper, we consider the problem of the recognition of various kinds of orderings produced by graph searches. To this aim, we introduce a new framework, the Tie-Breaking Label Search (TBLS), in order to handle a broad variety of…
Homomorphic encryption is a cryptographic paradigm allowing to compute on encrypted data, opening a wide range of applications in privacy-preserving data manipulation, notably in AI. Many of those applications require significant linear…
Depth First Search (DFS) tree is a fundamental data structure for solving graph problems. The DFS tree of a graph $G$ with $n$ vertices and $m$ edges can be built in $O(m+n)$ time. Till date, only a few algorithms have been designed for…