205877442
On distinct distance sets in a graph
A distinct distance set (DD set) for a graph G is a vertex subset of G with the property that for vbSvb = s, we have (2s) distinct distances of the pairs of vertices in S.In this article, it is shown that(a) For 6 ? k ? 18 there exists a tree T with DD(T) = k and dm(T) = LB(k) < B1(Kk), where LB(k) is the smallest value L for which there are positive integers A and B with A+B=k, A2+B2??L2?, AB??L2?.(b) For k ? 10, the minimum order of a tree T with DD(T) = k is B1(Kk), which is the order of the corresponding Colomb ruler for k.
10222228
The third Ramsey numbers for graphs with at most four edges
Abstract With the help of a computer, the Ramsey numbers r 3 ( H ) are obtained for each of the 19 graphs H with at most four edges and no isolated vertices.
39962298
Using Corpus Statistics to Remove Redundant Words in Text Categorization
This article studies aggressive word removal in text categorization to reduce the noise in free texts and to enhance the computational efficiency of categorization. We use a novel stop word identification method to automatically generate domain specific stoplists which are much larger than a conventional domain-independent stoplist. In our tests with three categorization methods on text collections from different domains/applications, significant numbers of words were removed without sacrificing categorization effectiveness. In the test of the Expert Network method on CACM documents, for example, an 87% removal of unique words reduced the vocabulary of documents from 8,002 distinct words to 1,045 words, which resulted in a 83% time savings and a 74% memory savings in the computation of category ranking, with a 10% precision improvement on average over not using word removal. It is evident in this study that automated word removal based on corpus statistics has a practical and significant impact on the computational tractability of categorization methods in large databases.
295949
A Study of Approaches to Hypertext Categorization
Hypertext poses new research challenges for text classification. Hyperlinks, HTML tags, category labels distributed over linked documents, and meta data extracted from related Web sites all provide rich information for classifying hypertext documents. How to appropriately represent that information and automatically learn statistical patterns for solving hypertext classification problems is an open question. This paper seeks a principled approach to providing the answers. Specifically, we define five hypertext regularities which may (or may not) hold in a particular application domain, and whose presence (or absence) may significantly influence the optimal design of a classifier. Using three hypertext datasets and three well-known learning algorithms (Naive Bayes, Nearest Neighbor, and First Order Inductive Learner), we examine these regularities in different domains, and compare alternative ways to exploit them. Our results show that the identification of hypertext regularities in the data and the selection of appropriate representations for hypertext in particular domains are crucial, but seldom obvious, in real-world problems. We find that adding the words in the linked neighborhood to the page having those links (both inlinks and outlinks) were helpful for all our classifiers on one data set, but more harmful than helpful for two out of the three classifiers on the remaining datasets. We also observed that extracting meta data from related Web sites was extremely useful for improving classification accuracy in some of those domains. Finally, the relative performance of the classifiers being tested provided insights into their strengths and limitations for solving classification problems involving diverse and often noisy Web pages.
5180938
A Sensor-cyber Network Testbed for Plume Detection, Identification, and Tracking
Detection, identification, and tracking (DIT) problems that arise in applications such as the protection of people and the environment against radiational, biological, and chemical plumes, can be solved by combining the modalities of sensor and cyber networks. The sensor network provides information about physical space activities, such as the locations and movements of plume sources and targets. The cyber network provides storage and computational resources to analyze and infer, based on realistic dispersion models of plumes with respect to physical phenomena (e.g., terrain and weather effects), where the plume originated, the trajectory of its movement (speed and direction), and the prediction of its future movement. The cyber network also makes decisions about where to task and activate plume sensors regarding their future sensing and communciation activities.
15017783
On the Computational Complexity of Sensor Network Localization
Determining the positions of the sensor nodes in a network is essential to many network functionalities such as routing, coverage and tracking, and event detection. The localization problem for sensor networks is to reconstruct the positions of all of the sensors in a network, given the distances between all pairs of sensors that are within some radius r of each other. In the past few years, many algorithms for solving the localization problem were proposed, without knowing the computational complexity of the problem. In this paper, we show that no polynomial-time algorithm can solve this problem in the worst case, even for sets of distance pairs for which a unique solution exists, unless RP = NP. We also discuss the consequences of our result and present open problems.
9199797
Error Detection and Impact-Sensitive Instance Ranking in Noisy Datasets
Given a noisy dataset, how to locate erroneous instances and attributes and rank suspicious instances based on their impacts on the system performance is an interesting and important research issue. We provide in this paper an Error Detection and Impact-sensitive instance Ranking (EDIR) mechanism to address this problem. Given a noisy dataset D, we first train a benchmark classifier T from D. The instances, that cannot be effectively classified by T are treated as suspicious and forwarded to a subset S. For each attribute Ai, we switch Ai and the class label C to train a classifier APi for Ai. Given an instance Ik in S, we use APi and the benchmark classifier T to locate the erroneous value of each attribute Ai. To quantitatively rank instances in S, we define an impact measure based on the Information-gain Ratio (IR). We calculate IRi between attribute Ai and C, and use IRi as the impact-sensitive weight of Ai. The sum of impact-sensitive weights from all located erroneous attributes of Ik indicates its total impact value. The experimental results demonstrate the effectiveness of our strategies.