Related papers: Enumerating Graph Partitions Without Too Small Con…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
There exist many orthogonal graph drawing algorithms that minimize edge crossings or edge bends, however they produce unsatisfactory drawings in many practical cases. In this paper we present a grid-based algorithm for drawing orthogonal…
Component-centric distributed graph processing platforms that use a bulk synchronous parallel (BSP) programming model have gained traction. These address the short-comings of Big Data abstractions/platforms like MapReduce/Hadoop for…
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
Subgraph matching is a fundamental problem in graph analysis with a wide range of applications. However, due to its inherent NP-hardness, enumerating subgraph matches efficiently on large real-world graphs remains highly challenging. Most…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and…
Sampling is a widely used graph reduction technique to accelerate graph computations and simplify graph visualizations. By comprehensively analyzing the literature on graph sampling, we assume that existing algorithms cannot effectively…
Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental…
We propose a novel algorithm for enumerating and listing all minimal cutsets of a given graph. It is known that this problem is NP-hard. We use connectivity properties of a given graph to develop an algorithm with reduced complexity for…
This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolation lemma as described in (Mulmuley et al. 1987) achieves the…
We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the…
Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…