Kun He

Uncovering the Small Community Structure in Large Networks: A Local Spectral Approach

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify the community from a few exemplary seed members. %Very few approaches can systematically demonstrate both high efficiency and effectiveness that significantly stands out amongst the divergent approaches in finding communities. In this paper, we propose a novel approach for finding overlapping communities called LEMON (Local Expansion via Minimum One Norm). Different from PageRank-like diffusion methods, LEMON finds the community by seeking a sparse vector in the span of the local spectra such that the seeds are in its support. We show that LEMON can achieve the highest detection accuracy among state-of-the-art proposals. The running time depends on the size of the community rather than that of the entire graph. The algorithm is easy to implement, and is highly parallelizable. Moreover, given that networks are not all similar in nature, a comprehensive analysis on how the local expansion approach is suited for uncovering communities in different networks is still lacking. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the quality and quantity of the seed set would affect the performance are provided.

An efficient deterministic heuristic for two-dimensional rectangular packing

This paper proposes a deterministic heuristic, a best fit algorithm (BFA), for solving the NP-hard two-dimensional rectangular packing problem to maximize the filling rate of a rectangular sheet. There are two stages in this new approach: the constructive stage and the tree search stage. The former aims to rapidly generate an initial solution by employing the concepts of action space and fit degree in evaluating different placements. The latter seeks to further improve the solution and searches for promising placements by a partial tree search procedure. We then compare BFA with other approaches in terms of solution quality and computing time. We carry out computational experiments on two sets of well-known benchmark instances, C21 proposed by Hopper and Turton, and N13 proposed by Burke et al. BFA gained an average filling rate of 100% for the C21 instances within short times, indicating that all the layouts obtained are optimal. To the best of our knowledge, this is the first time that optimal layouts on all the 21 instances were obtained by a deterministic algorithm. As for the N13 instances, to date, researchers have found optimal solutions to the first three instances, whereas BFA solved seven, including the first three, within a reasonable period. An additional work is to adapt BFA to solve a relevant problem, the constrained two-dimensional cutting (or packing) problem (CTDC). Though BFA is not for the CTDC in the original design such that some specific characteristics of CTDC are not considered, the adapted algorithm still performed well on 21 public CTDC instances.

A new heuristic algorithm for cuboids packing with no orientation constraints

The three-dimensional cuboids packing is NP-hard and finds many applications in the transportation industry. The problem is to pack a subset of cuboid boxes into a big cuboid container such that the total volume of the packed boxes is maximized. The boxes have no orientation constraints, i.e. they can be rotated by 90^@? in any direction. A new heuristic algorithm is presented that defines a conception of caving degree to judge how close a packing box is to those boxes already packed into the container, and always chooses a packing with the largest caving degree to do. The performance is evaluated on all the 47 related benchmarks from the OR-Library. Experiments on a personal computer show a high average volume utilization of 94.6% with an average computation time of 23min for the strengthened A1 algorithm, which improves current best records by 3.6%. In addition, the top-10 A2 algorithm achieved an average volume utilization of 91.9% with an average computation time of 55s, which also got higher utilization than current best records reported in the literature.

Heuristics for two-dimensional strip packing problem with 90° rotations

Abstract This paper proposes a deterministic heuristic algorithm (DHA) for two-dimensional strip packing problem where 90° rotations of pieces are allowed and there is no guillotine packing constraint. The objective is to place all pieces without overlapping into a strip of given width so as to minimize the total height of the pieces. Based on the definition of action space, a new sorting rule for candidate placements is proposed such that the position for the current piece is as low as possible, the distance between the current piece and other inside pieces is as close as possible, and the adverse impact for further placements is as little as possible. Experiments on four groups of benchmarks showed the proposed DHA achieved highly competitive results in comparison with the state-of-the-art algorithms in the literature. Also, as a deterministic algorithm, the DHA could achieve high quality solutions by only one independent run on both small-scale and large-scale problem instances and the results are repeatable.

Detecting Overlapping Communities from Local Spectral Subspaces

Based on the definition of local spectral subspace, we propose a novel approach called LOSP for local overlapping community detection. Using the power method for a few steps, LOSP finds an approximate invariant subspace, which depicts the embedding of the local neighborhood structure around the seeds of interest. LOSP then identifies the local community expanded from the given seeds by seeking a sparse indicator vector in the subspace where the seeds are in its support. We provide a systematic investigation on LOSP, and thoroughly evaluate it on large real world networks across multiple domains. With the prior information of very few seed members, LOSP can detect the remaining members of a target community with high accuracy. Experiments demonstrate that LOSP outperforms the Heat Kernel and PageRank diffusions. Using LOSP as a subroutine, we further address the problem of multiple membership identification, which aims to find all the communities a single vertex belongs to. High F1 scores are achieved in detecting multiple local communities with respect to arbitrary single seed for various large real world networks.

Dynamic reduction heuristics for the rectangle packing area minimization problem

The rectangle packing area minimization problem is a key sub-problem of floorplanning in VLSI design. This problem places a set of axis aligned two-dimensional rectangular items of given sizes onto a rectangular plane such that no two items overlap and the area of the enveloping rectangle is minimized. This paper presents a dynamic reduction algorithm that transforms an instance of the original problem to a series of instances of the rectangle packing problem by dynamically determining the dimensions of the enveloping rectangle. We define an injury degree to evaluate the possible negative impact for candidate placements, and we propose a least injury first approach for solving the rectangle packing problem. Next, we incorporate a compacting approach to compact the resulting layout by alternatively moving the items left and down toward a bottom-left corner such that we may obtain a smaller enveloping rectangle. We also show the feasibility, compactness, non-inferiority, and halting properties of the compacting approach. Comprehensive experiments were conducted on 11 MCNC and GSRC benchmarks and 28 instances reported in the literature. The experimental results show the high efficiency and effectiveness of the proposed dynamic reduction algorithm, especially on large-scale instances with hundreds of items.

An action-space-based global optimization algorithm for packing circles into a square container

This paper proposes an action-space-based global optimization (ASGO) approach for the problem of packing unequal circles into a square container such that the size of the square is minimized. Starting from several random configurations, ASGO runs the following potential descent method and basin-hopping strategy iteratively. It finds configurations with the local minimum potential energy by the limited-memory BFGS (LBFGS) algorithm, then selects the circular items having the most deformations and moves them to some large vacant space or randomly chosen vacant space. By adapting the action space defined for the rectangular packing problem, we approximate each circular item as a rectangular item, thus making it much easier to find comparatively larger vacant spaces for any given configuration. The tabu strategy is used to prevent cycling and enhance the diversification during the search procedure. Several other strategies, such as swapping two similar circles or swapping two circles in different quadrants in the container, are combined to increase the diversity of the configurations. We compare the performance of ASGO on 68 benchmark instances at the Packomania website with the state-of-the-art results. ASGO obtains configurations with smaller square containers on 63 instances; at the same time it matches or approaches the current best results on the other five instances.

Iterated Tabu Search and Variable Neighborhood Descent for Packing Unequal Circles into a Circular Container

This paper presents an Iterated Tabu Search and Variable Neighborhood Descent (ITS-VND) algorithm for packing unequal circles into a circular container (PUCC). The algorithm adapts the Tabu Search procedure of Iterated Tabu Search algorithms and proposes a Tabu Search and Variable Neighborhood Descent (TS-VND) procedure. We observe there are strong complementarities between the small circles and the large vacant places, and propose the insert neighborhood to match up the small circles with the large vacant places. Although the insert neighborhood is inefficient and time-consuming, it is an important supplement to the classic swap neighborhood as it could arrange the small circles properly. Predicated on these features, we employ the insert neighborhood only at chosen local minima of the swap neighborhood that shows promise for an improvement. The traditional Tabu Search procedure is then transformed into a hybrid procedure composed of two alternative parts, namely Variable Neighborhood Descent and Tabu Search respectively. Besides this reformed procedure, ITS-VND also incorporates other new features, such as an adaptive evaluation function, a novel method for accelerating the neighborhood exploration, and the “collision accidents” criterion for evaluating how intensively the area near the current solution has been explored. The computational results on three well established benchmark sets show that the proposed algorithm not only has a good discovery capability but also can provide good results within a reasonable time. For a total of 84 benchmark instances, the proposed algorithm improves the best-known results on 23 instances, matches 60, and only misses one.

Hidden community detection in social networks

Propose a new conception of hidden community for network analysis.Provide a meta-approach called HICODE for finding the hidden communities.Several weakening methods are proposed to reduce the impact of the detected structure.The framework works iteratively to enhance the detection on both dominant communities and hidden communities.Extensive experiments demonstrate the effectiveness of the proposed method. This paper introduces a new graph-theoretical concept of hidden community for analysing complex networks, which contain both stronger or dominant communities and weak communities. The weak communities are termed as being with the hidden community structure if most of its members also belong to the stronger communities. We propose a meta-approach, namely HICODE (HIdden COmmunity DEtection), for identifying the hidden community structure as well as enhancing the detection of the dominant community structure. Extensive experiments on real-world networks are carried out and the obtained results demonstrate that HICODE outperforms several state-of-the-art community detection methods in terms of uncovering both the dominant and the hidden structure. Due to the difficulty of labeling all ground truth communities in real-world datasets, HICODE provides a promising technique to pinpoint the existing latent communities and uncover communities for which there is no ground truth. Our finding in this work is significant to detect hidden communities in complex social networks.

A pure quasi-human algorithm for solving the cuboid packing problem

We excavate the wisdom from an old Chinese proverb “gold corner, silver side and strawy void”, and further improve it into “maximum value in diamond cave” for solving the NP-hard cuboid packing problem. We extract, integrate and formalize the idea by west modern mathematical tools, and propose a pure quasi-human algorithm. The performance of the algorithm is evaluated on two sets of public benchmarks. For 100 strongly heterogeneous difficult benchmarks, experiments show an average packing utilization of 87.31%, which surpasses current best record reported in the literature by 1.83%. For 47 difficult benchmarks without orientation constraint, experiments show an average volume utilization of 92.05%, which improves current best record reported in the literature by 1.05%.