Underestimated cost of targeted attacks on complex networks

The robustness of complex networks under targeted attacks is deeply connected to the resilience of complex systems, i.e., the ability to make appropriate responses to the attacks. In this article, we investigated the state-of-the-art targeted node attack algorithms and demonstrate that they become very inefficient when the cost of the attack is taken into consideration. In this paper, we made explicit assumption that the cost of removing a node is proportional to the number of adjacent links that are removed, i.e., higher degree nodes have higher cost. Finally, for the case when it is possible to attack links, we propose a simple and efficient edge removal strategy named Hierarchical Power Iterative Normalized cut (HPI-Ncut).The results on real and artificial networks show that the HPI-Ncut algorithm outperforms all the node removal and link removal attack algorithms when the cost of the attack is taken into consideration. In addition, we show that on sparse networks, the complexity of this hierarchical power iteration edge removal algorithm is only $O(n\log^{2+\epsilon}(n))$.Comment: 14 pages, 7 figure

Generalized Network Dismantling

Finding the set of nodes, which removed or (de)activated can stop the spread of (dis)information, contain an epidemic or disrupt the functioning of a corrupt/criminal organization is still one of the key challenges in network science. In this paper, we introduce the generalized network dismantling problem, which aims to find the set of nodes that, when removed from a network, results in a network fragmentation into subcritical network components at minimum cost. For unit costs, our formulation becomes equivalent to the standard network dismantling problem. Our non-unit cost generalization allows for the inclusion of topological cost functions related to node centrality and non-topological features such as the price, protection level or even social value of a node. In order to solve this optimization problem, we propose a method, which is based on the spectral properties of a novel node-weighted Laplacian operator. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens new directions in understanding the vulnerability and robustness of complex systems.Comment: 6 pages, 5 figure

An Efficient Algorithm for Sparse Quantum State Preparation

Generating quantum circuits that prepare specific states is an essential part of quantum compilation. Algorithms that solve this problem for general states generate circuits at grow exponentially in the number of qubits. However, in contrast to general states, many practically relevant states are sparse in the standard basis. In this paper we show how sparsity can be used for efficient state preparation. We present a polynomial-time algorithm that generates polynomial-size quantum circuits (linear in the number of nonzero coefficients times number of qubits) that prepare given states, making computer-aided design of sparse state preparation scalable

The Red-Blue Pebble Game on Trees and DAGs with Large Input

Data movements between different levels of a memory hierarchy (I/Os) are a principal performance bottleneck. This is particularly noticeable in computations that have low complexity but large amounts of input data, often occurring in “big data”. Using the red-blue pebble game, we investigate the I/O-complexity of directed acyclic graphs (DAGs) with a large proportion of input vertices. For trees, we show that the number of leaves is a 2-approximation for the optimal number of I/Os. Similar techniques as we use in the proof of the results for trees allow us to find lower and upper bounds of the optimal number of I/Os for general DAGs. The larger the proportion of input vertices, the stronger those bounds become. For families of DAGs with bounded degree and a large proportion of input vertices (meaning that there exists some constant c>0 such that for every DAG G of this family, the proportion p of input vertices satisfies p>c) our bounds give constant factor approximations, improving the previous logarithmic approximation factors. For those DAGs, by avoiding certain I/O-inefficiencies, which we will define precisely, a pebbling strategy is guaranteed to satisfy those bounds and asymptotics. We extend the I/O-bounds for trees to a multiprocessor setting with fast individual memories and a slow shared memory.ISSN:0302-9743ISSN:1611-334

I/O-Optimal Cache-Oblivious Sparse Matrix-Sparse Matrix Multiplication

Data movements between different levels of the memory hierarchy (I/O-transitions, or simply I/Os) are a critical performance bottleneck in modern computing. Therefore it is a problem of high practical relevance to find algorithms that use a minimal number of I/Os. We present a cache-oblivious sparse matrix-sparse matrix multiplication algorithm that uses a worst-case number of I/Os that matches a previously established lower bound for this problem (O (N-2/B.M) read-I/Os and O (N-2/B) write-I/Os, where N is the size of the problem instance, M is the size of the fast memory and B is the size of the cache lines). When the output does not need to be stored, also the number of write-I/Os can be reduced to O (N-2/B.M). This improves the worst-case DO-complexity of the previously best known algorithm for this problem (which is cache-aware) by a logarithmic multiplicative factor. Compared to other cache-oblivious algorithms our algorithm improves the worst-case number of I/Os by a multiplicative factor of Theta(M . N). We show how the algorithm can be applied to produce the first I/O-efficient solution for the sparse 2- vs 3-diameter problem on sparse directed graphs

Generalized Network Dismantling

Finding the set of nodes, which removed or (de)activated can stop the spread of (dis)information, contain an epidemic or disrupt the functioning of a corrupt/criminal organization is still one of the key challenges in network science. In this paper, we introduce the generalized network dismantling problem, which aims to find the set of nodes that, when removed from a network, results in a network fragmentation into subcritical network components at minimum cost. For unit costs, our formulation becomes equivalent to the standard network dismantling problem. Our non-unit cost generalization allows for the inclusion of topological cost functions related to node centrality and non-topological features such as the price, protection level or even social value of a node. In order to solve this optimization problem, we propose a method, which is based on the spectral properties of a novel node-weighted Laplacian operator. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens new directions in understanding the vulnerability and robustness of complex systems

ProbGraph: High-Performance and High-Accuracy Graph Mining with Probabilistic Set Representations

Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with strong theoretical guarantees on work, depth, and result accuracy. The key idea is to represent sets of vertices using probabilistic set representations such as Bloom filters. These representations are much faster to process than the original vertex sets thanks to vectorizability and small size. We use these representations as building blocks in important parallel graph mining algorithms such as Clique Counting or Clustering. When enhanced with ProbGraph, these algorithms significantly outperform tuned parallel exact baselines (up to nearly 50x on 32 cores) while ensuring accuracy of more than 90% for many input graph datasets. Our novel bounds and algorithms based on probabilistic set representations with desirable statistical properties are of separate interest for the data analytics community