DDSL: Efficient Subgraph Listing on Distributed and Dynamic Graphs

Subgraph listing is a fundamental problem in graph theory and has wide applications in areas like sociology, chemistry, and social networks. Modern graphs can usually be large-scale as well as highly dynamic, which challenges the efficiency of existing subgraph listing algorithms. Recent works have shown the benefits of partitioning and processing big graphs in a distributed system, however, there is only few work targets subgraph listing on dynamic graphs in a distributed environment. In this paper, we propose an efficient approach, called Distributed and Dynamic Subgraph Listing (DDSL), which can incrementally update the results instead of running from scratch. DDSL follows a general distributed join framework. In this framework, we use a Neighbor-Preserved storage for data graphs, which takes bounded extra space and supports dynamic updating. After that, we propose a comprehensive cost model to estimate the I/O cost of listing subgraphs. Then based on this cost model, we develop an algorithm to find the optimal join tree for a given pattern. To handle dynamic graphs, we propose an efficient left-deep join algorithm to incrementally update the join results. Extensive experiments are conducted on real-world datasets. The results show that DDSL outperforms existing methods in dealing with both static dynamic graphs in terms of the responding time

On the Algebraic Proof Complexity of Tensor Isomorphism

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 problem, TI (or rather, proving that two tensors are non-isomorphic) lends itself very naturally to algebraic and semi-algebraic proof systems, such as the Polynomial Calculus (PC) and Sum of Squares (SoS). For its combinatorial cousin Graph Isomorphism, essentially optimal lower bounds are known for approaches based on PC and SoS (Berkholz & Grohe, SODA'17). Our main results are an Ω(n) lower bound on PC degree or SoS degree for Tensor Isomorphism, and a nontrivial upper bound for testing isomorphism of tensors of bounded rank. We also show that PC cannot perform basic linear algebra in sub-linear degree, such as comparing the rank of two matrices (which is essentially the same as 2-TI), or deriving BA = I from AB = I. As linear algebra is a key tool for understanding tensors, we introduce a strictly stronger proof system, PC+Inv, which allows as derivation rules all substitution instances of the implication AB = I → BA = I. We conjecture that even PC+Inv cannot solve TI in polynomial time either, but leave open getting lower bounds on PC+Inv for any system of equations, let alone those for TI. We also highlight many other open questions about proof complexity approaches to TI

ON THE COMPLEXITY OF ISOMORPHISM PROBLEMS FOR TENSORS, GROUPS, AND POLYNOMIALS I: TENSOR ISOMORPHISM-COMPLETENESS

We study the complexity of isomorphism problems for tensors, groups, and polynomials. These problems have been studied in multivariate cryptography, machine learning, quantum information, and computational group theory. We show that these problems are all polynomial-time equivalent, creating bridges between problems traditionally studied in myriad research areas. This prompts us to define the complexity class TI, namely problems that reduce to the tensor isomorphism problem in polynomial time. Our main technical result is a polynomial-time reduction from d-tensor isomorphism to 3-tensor isomorphism. In the context of quantum information, this result gives a multipartite-to-tripartite entanglement transformation procedure that preserves equivalence under stochastic local operations and classical communication

Towards learning inverse kinematics with a neural network based tracking controller

Learning an inverse kinematic model of a robot is a well studied subject. However, achieving this without information about the geometric characteristics of the robot is less investigated. In this work, a novel control approach is presented based on a recurrent neural network. Without any prior knowledge about the robot, this control strategy learns to control the iCub’s robot arm online by solving the inverse kinematic problem in its control region. Because of its exploration strategy the robot starts to learn by generating and observing random motor behavior. The modulation and generalization capabilities of this approach are investigated as well

The Index-Based Subgraph Matching Algorithm (ISMA): Fast Subgraph Enumeration in Large Networks Using Optimized Search Trees

Subgraph matching algorithms are designed to find all instances of predefined subgraphs in a large graph or network and play an important role in the discovery and analysis of so-called network motifs, subgraph patterns which occur more often than expected by chance. We present the index-based subgraph matching algorithm (ISMA), a novel tree-based algorithm. ISMA realizes a speedup compared to existing algorithms by carefully selecting the order in which the nodes of a query subgraph are investigated. In order to achieve this, we developed a number of data structures and maximally exploited symmetry characteristics of the subgraph. We compared ISMA to a naive recursive tree-based algorithm and to a number of well-known subgraph matching algorithms. Our algorithm outperforms the other algorithms, especially on large networks and with large query subgraphs. An implementation of ISMA in Java is freely available at http://sourceforge.net/projects/isma

Ecogeographical rules and the macroecology of food webs

AimHow do factors such as space, time, climate and other ecological drivers influence food web structure and dynamics? Collections of well‐studied food webs and replicate food webs from the same system that span biogeographical and ecological gradients now enable detailed, quantitative investigation of such questions and help integrate food web ecology and macroecology. Here, we integrate macroecology and food web ecology by focusing on how ecogeographical rules [the latitudinal diversity gradient (LDG), Bergmann’s rule, the island rule and Rapoport’s rule] are associated with the architecture of food webs.LocationGlobal.Time periodCurrent.Major taxa studiedAll taxa.MethodsWe discuss the implications of each ecogeographical rule for food webs, present predictions for how food web structure will vary with each rule, assess empirical support where available, and discuss how food webs may influence ecogeographical rules. Finally, we recommend systems and approaches for further advancing this research agenda.ResultsWe derived testable predictions for some ecogeographical rules (e.g. LDG, Rapoport’s rule), while for others (e.g., Bergmann’s and island rules) it is less clear how we would expect food webs to change over macroecological scales. Based on the LDG, we found weak support for both positive and negative relationships between food chain length and latitude and for increased generality and linkage density at higher latitudes. Based on Rapoport’s rule, we found support for the prediction that species turnover in food webs is inversely related to latitude.Main conclusionsThe macroecology of food webs goes beyond traditional approaches to biodiversity at macroecological scales by focusing on trophic interactions among species. The collection of food web data for different types of ecosystems across biogeographical gradients is key to advance this research agenda. Further, considering food web interactions as a selection pressure that drives or disrupts ecogeographical rules has the potential to address both mechanisms of and deviations from these macroecological relationships. For these reasons, further integration of macroecology and food webs will help ecologists better understand the assembly, maintenance and change of ecosystems across space and time.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151318/1/geb12925_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151318/2/geb12925.pd