Related papers: Towards a Decomposition-Optimal Algorithm for Coun…
For a graph $G$, let $Z(G,\lambda)$ be the partition function of the monomer-dimer system defined by $\sum_k m_k(G)\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and online social networks (OSNs). Nowadays the massive size of…
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the…
Counting small patterns in a large dataset is a fundamental algorithmic task. The most common version of this task is subgraph/homomorphism counting, wherein we count the number of occurrences of a small pattern graph $H$ in an input graph…
Motivated by longstanding conjectures regarding decompositions of graphs into paths and cycles, we prove the following optimal decomposition results for random graphs. Let $0<p<1$ be constant and let $G\sim G_{n,p}$. Let $odd(G)$ be the…
Uniform sampling and approximate counting are fundamental primitives for modern database applications, ranging from query optimization to approximate query processing. While recent breakthroughs have established optimal sampling and…
The randomized technique of color coding is behind state-of-the-art algorithms for estimating graph motif counts. Those algorithms, however, are not yet capable of scaling well to very large graphs with billions of edges. In this paper we…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
In classic distributed graph problems, each instance on a graph specifies a space of feasible solutions (e.g. all proper ($\Delta+1$)-list-colorings of the graph), and the task of distributed algorithm is to construct a feasible solution…
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and…
We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise $\epsilon$-close to the uniform distribution, in an \emph{amortized-efficient} fashion. We consider the adjacency list…
Core decomposition is a classic technique for discovering densely connected regions in a graph with large range of applications. Formally, a $k$-core is a maximal subgraph where each vertex has at least $k$ neighbors. A natural extension of…
As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…
We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our…
We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Classical works by Lov\'asz show that many interesting quantities have this form, including, for fixed…
We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…
Given a join with an acyclic set of degree constraints, we show how to draw a uniformly random sample from the join result in $O(\mathit{polymat}/ \max \{1, \mathrm{OUT} \})$ expected time after a preprocessing of $O(\mathrm{IN})$ expected…
A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…