Linear-time heuristic partitioning technique for mapping of connected graphs into single-row networks

In this paper, a model called graph partitioning and transformation model (GPTM) which transforms a connected graph into a single-row network is introduced. The transformation is necessary in applications such as in the assignment of telephone channels to caller-receiver pairs roaming in cells in a cellular network on real-time basis. A connected graph is then transformed into its corresponding single-row network for assigning the channels to the caller-receiver pairs. The GPTM starts with the linear-time heuristic graph partitioning to produce two subgraphs with higher densities. The optimal labeling for nodes are then formed based on the simulated annealing technique. Experimental results support our hypothesis that GPTM efficiently transforms the connected graph into its single-row network

Isomorphic bisections of cubic graphs

Graph partitioning, or the dividing of a graph into two or more parts based on certain conditions, arises naturally throughout discrete mathematics, and problems of this kind have been studied extensively. In the 1990s, Ando conjectured that the vertices of every cubic graph can be partitioned into two parts that induce isomorphic subgraphs. Using probabilistic methods together with delicate recolouring arguments, we prove Ando's conjecture for large connected graphs

Computational Optimization Techniques for Graph Partitioning

Partitioning graphs into two or more subgraphs is a fundamental operation in computer science, with applications in large-scale graph analytics, distributed and parallel data processing, and fill-reducing orderings in sparse matrix algorithms. Computing balanced and minimally connected subgraphs is a common pre-processing step in these areas, and must therefore be done quickly and efficiently. Since graph partitioning is NP-hard, heuristics must be used. These heuristics must balance the need to produce high quality partitions with that of providing practical performance. Traditional methods of partitioning graphs rely heavily on combinatorics, but recent developments in continuous optimization formulations have led to the development of hybrid methods that combine the best of both approaches. This work describes numerical optimization formulations for two classes of graph partitioning problems, edge cuts and vertex separators. Optimization-based formulations for each of these problems are described, and hybrid algorithms combining these optimization-based approaches with traditional combinatoric methods are presented. Efficient implementations and computational results for these algorithms are presented in a C++ graph partitioning library competitive with the state of the art. Additionally, an optimization-based approach to hypergraph partitioning is proposed

Balanced Crown Decomposition for Connectivity Constraints

We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local nature of the connectivity condition usually results in very challenging algorithmic tasks. The balanced crown decomposition is a combination of a crown decomposition and a balanced partition which makes it applicable to graph editing as well as graph packing and partitioning problems. We illustrate this by deriving improved approximation algorithms and kernelization for a variety of such problems. In particular, through this structure, we obtain the first constant-factor approximation for the Balanced Connected Partition (BCP) problem, where the task is to partition a vertex-weighted graph into k connected components of approximately equal weight. We derive a 3-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component

Computational Optimization Techniques for Graph Partitioning

Partitioning graphs into two or more subgraphs is a fundamental operation in computer science, with applications in large-scale graph analytics, distributed and parallel data processing, and fill-reducing orderings in sparse matrix algorithms. Computing balanced and minimally connected subgraphs is a common pre-processing step in these areas, and must therefore be done quickly and efficiently. Since graph partitioning is NP-hard, heuristics must be used. These heuristics must balance the need to produce high quality partitions with that of providing practical performance. Traditional methods of partitioning graphs rely heavily on combinatorics, but recent developments in continuous optimization formulations have led to the development of hybrid methods that combine the best of both approaches. This work describes numerical optimization formulations for two classes of graph partitioning problems, edge cuts and vertex separators. Optimization-based formulations for each of these problems are described, and hybrid algorithms combining these optimization-based approaches with traditional combinatoric methods are presented. Efficient implementations and computational results for these algorithms are presented in a C++ graph partitioning library competitive with the state of the art. Additionally, an optimization-based approach to hypergraph partitioning is proposed

Robust Group Linkage

We study the problem of group linkage: linking records that refer to entities in the same group. Applications for group linkage include finding businesses in the same chain, finding conference attendees from the same affiliation, finding players from the same team, etc. Group linkage faces challenges not present for traditional record linkage. First, although different members in the same group can share some similar global values of an attribute, they represent different entities so can also have distinct local values for the same or different attributes, requiring a high tolerance for value diversity. Second, groups can be huge (with tens of thousands of records), requiring high scalability even after using good blocking strategies. We present a two-stage algorithm: the first stage identifies cores containing records that are very likely to belong to the same group, while being robust to possible erroneous values; the second stage collects strong evidence from the cores and leverages it for merging more records into the same group, while being tolerant to differences in local values of an attribute. Experimental results show the high effectiveness and efficiency of our algorithm on various real-world data sets