Related papers: Linear-Time Graph Programs without Preconditions
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…
Optimizing the execution time of tensor program, e.g., a convolution, involves finding its optimal configuration. Searching the configuration space exhaustively is typically infeasible in practice. In line with recent research using TVM, we…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
Graph pattern matching, which aims to discover structural patterns in graphs, is considered one of the most fundamental graph mining problems in many real applications. Despite previous efforts, existing systems face two main challenges.…
A linear graph is a graph whose vertices are totally ordered. Biological and linguistic sequences with interactions among symbols are naturally represented as linear graphs. Examples include protein contact maps, RNA secondary structures…
This papers defines the syntax and semantics of GP 2, a revised version of the graph programming language GP. New concepts are illustrated and explained with example programs. Changes to the first version of GP include an improved type…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
With the rapid growth of unstructured and semistructured data, parallelizing graph algorithms has become essential for efficiency. However, due to the inherent irregularity in computation, memory access patterns, and communication, graph…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For $m$-edge and $n$-vertex graphs, it is well-known to be solvable in $O(m\sqrt{n})$ time; however, for several applications…
We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a structure that is desirable in many aspects. While much…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
In this work we target the problem of provably computing the equivalence between two programs represented as dataflow graphs. To this end, we formalize the problem of equivalence between two programs as finding a set of semantics-preserving…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
We show theoretically and empirically that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems such as electric flow and eigenvector decomposition. The Transformer has access to…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Many graph problems can be solved using ordered parallel graph algorithms that achieve significant speedup over their unordered counterparts by reducing redundant work. This paper introduces a new priority-based extension to GraphIt, a…
Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…
We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…