Related papers: On the Complexity of Triangle Counting using Empti…
In 2009, Kong, Wang, and Lee began work on the problem of finding the edge-balanced index sets (EBI) of complete bipartite graphs K_{m,n} by solving the cases where n = 1, 2, 3, 4, and 5, and also the case where m = n. In 2011, Krop and…
Many common graph data mining tasks take the form of identifying dense subgraphs (e.g. clustering, clique-finding, etc). In biological applications, the natural model for these dense substructures is often a complete bipartite graph…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard problem. A popular way to study WIS is to detect graph classes for which WIS can be solved in polynomial time, with particular reference to hereditary graph classes,…
Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
Given an unknown $n \times n$ matrix $A$ having non-negative entries, the \emph{inner product} (IP) oracle takes as inputs a specified row (or a column) of $A$ and a vector $v \in \mathbb{R}^{n}$, and returns their inner product. A…
This paper addresses the problem of improving the query performance of the triangular expansion algorithm (TEA) for computing visibility regions by finding the most advantageous instance of the triangular mesh, the preprocessing structure.…
In the context of changing travel behaviors and the expanding user base of Geographic Information System (GIS) services, conventional centralized architectures responsible for handling shortest distance queries are facing increasing…
Bi-quadratic programming over unit spheres is a fundamental problem in quantum mechanics introduced by pioneer work of Einstein, Schr\"odinger, and others. It has been shown to be NP-hard; so it must be solve by efficient heuristic…
Maximal biclique enumeration is a fundamental problem in bipartite graph data analysis. Existing biclique enumeration methods mainly focus on non-attributed bipartite graphs and also ignore the \emph{fairness} of graph attributes. In this…
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm…
How can we effectively and efficiently learn node representations in signed bipartite graphs? A signed bipartite graph is a graph consisting of two nodes sets where nodes of different types are positively or negative connected, and it has…
We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS)…
The Tensor Isomorphism problem (TI) has recently emerged as having connections to multiple areas of research within complexity and beyond, but the current best upper bound is essentially the brute force algorithm. Being an algebraic…
We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of…
Edge detection (ED) is a fundamental perceptual process in computer vision, forming the structural basis for high-level reasoning tasks such as segmentation, recognition, and scene understanding. Despite substantial progress achieved by…
By far the most fruitful technique for showing lower bounds for the CONGEST model is reductions to two-party communication complexity. This technique has yielded nearly tight results for various fundamental problems such as distance…
We consider the maximum bipartite matching problem in stochastic settings, namely the query-commit and price-of-information models. In the query-commit model, an edge e independently exists with probability $p_e$. We can query whether an…
Complete enumeration of finite models of first-order logic (FOL) formulas is pivotal to universal algebra, which studies and catalogs algebraic structures. Efficient finite model enumeration is highly challenging because the number of…