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**1 - 2**of**2**### Research Statement

"... As people rely more and more on computers, building and maintaining a secure computing environment becomes one of the most important research topics. However, many computer programs remain vulnerable, which makes intrusions to a computer or a network of computers easy. The number of vulnerabilities ..."

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As people rely more and more on computers, building and maintaining a secure computing environment becomes one of the most important research topics. However, many computer programs remain vulnerable, which makes intrusions to a computer or a network of computers easy. The number of vulnerabilities reported to CERT 1 grows rapidly from 1090 in the year of 2000 to 5990 in 2005. According to SecurityTracker 2, buffer overflows top the list at more than half of the vulnerabilities reported in 2004. Vulnerabilities like buffer overflows may permit an attacker to inject attack code, and cause the vulnerable machine to run the attacker’s program, instead. Detecting such intrusions is critical in securing a computer system. I have been working on host-based intrusion detections for my Ph.D. thesis, and my research interests are in computer security and network security. 0.1 Recent Research Results Intrusion detection systems can be categorized into signature-based and anomaly-based systems. Signature-based systems maintain an up-to-date database of intrusion signatures, and look for behavior that matches the signatures. Anomaly-based systems, on the other hand, maintain a normal behavior model and look for deviations from that model. Although signature-based techniques are

### THE EMERGENCE OF SPARSE SPANNERS AND WELL-SEPARATED PAIR DECOMPOSITION UNDER ANARCHY

- JOURNAL OF COMPUTATIONAL GEOMETRY
, 2012

"... A spanner graph on a set of points in Rd provides shortest paths between any pair of points with lengths at most a constant factor of their Euclidean distance. A spanner with a sparse set of edges is thus a good candidate for network backbones, as desired in many practical scenarios such as the tra ..."

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A spanner graph on a set of points in Rd provides shortest paths between any pair of points with lengths at most a constant factor of their Euclidean distance. A spanner with a sparse set of edges is thus a good candidate for network backbones, as desired in many practical scenarios such as the transportation network and peer-to-peer network overlays. In this paper we investigate new models and aim to interpret why good spanners ‘emerge ’ in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. We show that the following algorithm of constructing an edge pq, if and only if there is no existing edge p ′ q ′ with p ′ and q ′ at 1 distances no more than 4(1+1/ε) · |pq | from p, q respectively, generates a (1 + ε)-spanner with a linear number of edges. The algorithm also implies a simple algorithm for constructing linear-size well-separated pair decompositions that may of interest on their own. This new spanner construction algorithm has applications in the construction of nice network topologies for peer-to-peer systems, when peers join and leave the network and has only limited information about the rest of the network.