Space-filling curves and their use in the design of geometric data structures

Asano, Tomohiko; Ranjan, Desh; Roos, Thomas; Welzl, Emo; Widmayer, Peter

doi:10.1016/s0304-3975(96)00259-9

Cited by 195 publications

(94 citation statements)

References 4 publications

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“…Using the above method and by applying a small computer program 3 to the case k = 8 , We h a v e also applied the above technique to the three variants of a 3-D Hilbert indexing shown in Fig. 11.…”

Section: -D Hilbert Indexingsmentioning

confidence: 99%

Towards optimal locality in mesh-indexings

Niedermeier

Reinhardt

Sanders³

1997

Fundamentals of Computation Theory

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The e ciency of many data structures and algorithms relies on locality-preserving" indexing schemes for meshes. We concentrate on the case where the maximal distance between two mesh nodes indexed i and j shall be a slow-growing function of ji,jj. W e present a new 2-D indexing scheme we call H-indexing, which has superior supposedly optimal locality in comparison with the well-known Hilbert indexings. H-indexings form a Hamiltonian cycle and we prove that they are optimally locality-preserving among all cyclic indexings. We provide fairly tight l o w er bounds for indexings without any restriction. Further investigations include lower bound results for 3-D mesh indexings. Finally, exempli ed b y i n v estigations concerning 2-D and 3-D Hilbert indexings, we present a framework for mechanizing upper bound proofs for locality.

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Section: -D Hilbert Indexingsmentioning

confidence: 99%

Towards optimal locality in mesh-indexings

Niedermeier

Reinhardt

Sanders³

1997

Fundamentals of Computation Theory

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“…In this preliminary experiment, IP addresses are projected on a Hilbert curve [31] to visually confirm the locality of malicious IP addresses. Hilbert curve is a recursively defined space-filling curve.…”

Section: Address Space Skewnessmentioning

confidence: 99%

Analyzing Spatial Structure of IP Addresses for Detecting Malicious Websites

Chiba

Tobe

Mori

et al. 2013

Journal of Information Processing

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Web-based malware attacks have become one of the most serious threats that need to be addressed urgently. Several approaches that have attracted attention as promising ways of detecting such malware include employing one of several blacklists. However, these conventional approaches often fail to detect new attacks owing to the versatility of malicious websites. Thus, it is difficult to maintain up-to-date blacklists with information for new malicious websites. To tackle this problem, this paper proposes a new scheme for detecting malicious websites using the characteristics of IP addresses. Our approach leverages the empirical observation that IP addresses are more stable than other metrics such as URLs and DNS records. While the strings that form URLs or DNS records are highly variable, IP addresses are less variable, i.e., IPv4 address space is mapped onto 4-byte strings. In this paper, a lightweight and scalable detection scheme that is based on machine learning techniques is developed and evaluated. The aim of this study is not to provide a single solution that effectively detects web-based malware but to develop a technique that compensates the drawbacks of existing approaches. The effectiveness of our approach is validated by using real IP address data from existing blacklists and real traffic data on a campus network. The results demonstrate that our scheme can expand the coverage/accuracy of existing blacklists and also detect unknown malicious websites that are not covered by conventional approaches.

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“…In this context space filling curves are often used as a tool to determine very quickly data distribution layouts that guarantee good geometric locality [14][22] [24]. Space filling curves [27] have been also used in a wide variety of applications [3] both because of their hierarchical fractal structure as well as for their spatial locality properties. The most popular is the Hilbert curve [15], which guarantees the best geometric locality properties [23].…”

Section: Previous Workmentioning

confidence: 99%

Global static indexing for real-time exploration of very large regular grids

Pascucci

Frank

2001

Proceedings of the 2001 ACM/IEEE Conference on Supercomputing

109

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In this paper we introduce a new indexing scheme for progressive traversal and visualization of large regular grids. We demonstrate the potential of our approach by providing a tool that displays at interactive rates planar slices of scalar field data with very modest computing resources. We obtain unprecedented results both in terms of absolute performance and, more importantly, in terms of scalability. On a laptop computer we provide real time interaction with a 2048 3 grid (8 Giga-nodes) using only 20MB of memory. On an SGI Onyx we slice interactively an 8192 3 grid (½ tera-nodes) using only 60MB of memory. The scheme relies simply on the determination of an appropriate reordering of the rectilinear grid data and a progressive construction of the output slice. The reordering minimizes the amount of I/O performed during the out-of-core computation. The progressive and asynchronous computation of the output provides flexible quality/speed tradeoffs and a timecritical and interruptible user interface.

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Space-filling curves and their use in the design of geometric data structures

Cited by 195 publications

References 4 publications

Towards optimal locality in mesh-indexings

Towards optimal locality in mesh-indexings

Analyzing Spatial Structure of IP Addresses for Detecting Malicious Websites

Global static indexing for real-time exploration of very large regular grids

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