Related papers: Algorithms for Enumerating Balanced Tanner Graphs
We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…
Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…
We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…
The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on…
Classifying nodes in a graph is a common problem. The ideal classifier must adapt to any imbalances in the class distribution. It must also use information in the clustering structure of real-world graphs. Existing Graph Neural Networks…
A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a construction to show that there are infinitely many…
The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…
In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree…
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…
A D2CS of a graph G is a set $S \subseteq V(G)$ with $diam(G[S]) \leq 2$. We study the problem of counting and enumerating D2CS of a graph. First we give an explicit formula for the number of D2CS in a complete k-ary tree, Fibonacci tree,…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world…
An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…
This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived.…
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…
There is substantial literature dealing with fixed parameter algorithms for the dominating set problem on various families of graphs. In this paper, we give a $k^{O(dk)} n$ time algorithm for finding a dominating set of size at most $k$ in…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…
An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus…