Security of Graph Data: Hashing Schemes and Definitions

Use of graph-structured data models is on the rise - in graph databases, in representing biological and healthcare data as well as geographical data. In order to secure graph-structured data, and develop cryptographically secure schemes for graph databases, it is essential to formally define and develop suitable collision resistant one-way hashing schemes and show them they are efficient. The widely used Merkle hash technique is not suitable as it is, because graphs may be directed acyclic ones or cyclic ones. In this paper, we are addressing this problem. Our contributions are: (1) define the practical and formal security model of hashing schemes for graphs, (2) define the formal security model of perfectly secure hashing schemes, (3) describe constructions of hashing and perfectly secure hashing of graphs, and (4) performance results for the constructions. Our constructions use graph traversal techniques, and are highly efficient for hashing, redaction, and verification of hashes graphs. We have implemented the proposed schemes, and our performance analysis on both real and synthetic graph data sets support our claims

On Compact Routing for the Internet

While there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer routing tables of sizes that scale logarithmically with the network size, we demonstrate in this paper that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic routing table size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802

On The Effect of Hyperedge Weights On Hypergraph Learning

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms

Organic Design of Massively Distributed Systems: A Complex Networks Perspective

The vision of Organic Computing addresses challenges that arise in the design of future information systems that are comprised of numerous, heterogeneous, resource-constrained and error-prone components or devices. Here, the notion organic particularly highlights the idea that, in order to be manageable, such systems should exhibit self-organization, self-adaptation and self-healing characteristics similar to those of biological systems. In recent years, the principles underlying many of the interesting characteristics of natural systems have been investigated from the perspective of complex systems science, particularly using the conceptual framework of statistical physics and statistical mechanics. In this article, we review some of the interesting relations between statistical physics and networked systems and discuss applications in the engineering of organic networked computing systems with predictable, quantifiable and controllable self-* properties.Comment: 17 pages, 14 figures, preprint of submission to Informatik-Spektrum published by Springe

Efficient Micro-Mobility using Intra-domain Multicast-based Mechanisms (M&M)

One of the most important metrics in the design of IP mobility protocols is the handover performance. The current Mobile IP (MIP) standard has been shown to exhibit poor handover performance. Most other work attempts to modify MIP to slightly improve its efficiency, while others propose complex techniques to replace MIP. Rather than taking these approaches, we instead propose a new architecture for providing efficient and smooth handover, while being able to co-exist and inter-operate with other technologies. Specifically, we propose an intra-domain multicast-based mobility architecture, where a visiting mobile is assigned a multicast address to use while moving within a domain. Efficient handover is achieved using standard multicast join/prune mechanisms. Two approaches are proposed and contrasted. The first introduces the concept proxy-based mobility, while the other uses algorithmic mapping to obtain the multicast address of visiting mobiles. We show that the algorithmic mapping approach has several advantages over the proxy approach, and provide mechanisms to support it. Network simulation (using NS-2) is used to evaluate our scheme and compare it to other routing-based micro-mobility schemes - CIP and HAWAII. The proactive handover results show that both M&M and CIP shows low handoff delay and packet reordering depth as compared to HAWAII. The reason for M&M's comparable performance with CIP is that both use bi-cast in proactive handover. The M&M, however, handles multiple border routers in a domain, where CIP fails. We also provide a handover algorithm leveraging the proactive path setup capability of M&M, which is expected to outperform CIP in case of reactive handover.Comment: 12 pages, 11 figure

Compact Routing on Internet-Like Graphs

The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme on random graphs with power-law node degree distributions, $P_k \sim k^{-\gamma}$. We find that the average stretch is very low and virtually independent of $\gamma$. In particular, for the Internet interdomain graph, $\gamma \sim 2.1$, the average stretch is around 1.1, with up to 70% of paths being shortest. As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for $10^4$-node networks. Furthermore, we find that both the average shortest path length (i.e. distance) $\bar{d}$ and width of the distance distribution $\sigma$ observed in the real Internet inter-AS graph have values that are very close to the minimums of the average stretch in the $\bar{d}$- and $\sigma$-directions. This leads us to the discovery of a unique critical quasi-stationary point of the average TZ stretch as a function of $\bar{d}$ and $\sigma$. The Internet distance distribution is located in a close neighborhood of this point. This observation suggests the analytical structure of the average stretch function may be an indirect indicator of some hidden optimization criteria influencing the Internet's interdomain topology evolution.Comment: 29 pages, 16 figure