Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: Improved matching of a regular expression in an input string. A system first identifies a number of substrings (k) in a regular expression of length (m). The system receives a stream of start states for each of the substrings generated according to a regular expression matching process and receives a stream of end occurrences generated according to a multi-string matching process. The system identifies all instances where an end occurrence of a particular substring matches a positive start state of the particular substring, and enters the instances as positive substring accept states in the regular expression matching process on the input string. In one aspect, the system is much more efficient when (k) is much less than (m). The system can match the regular expression based on a bit offset between the first and second stream.

Abstract: A current key is received at a current arrival time at a computer. An index in an array corresponding to the current key is determined using a hash function. A previous key and a previous arrival time are retrieved from the array at the index. The array is transformed by replacing the previous key and the previous arrival time with the current key and the current arrival time in the array at the index. The previous key and the previous arrival time are inserted into a nearest eligible sequential index in the array.

Abstract: Methods, systems, and products describe a robust solution for the dictionary problem of data structures. A hash function based on tabulation is twisted to utilize an additional xoring operation and a shift. This twisted tabulation offers strong robustness guarantees over a set of queries in both linear probing and chaining.

Abstract: A current key is received at a current arrival time at a computer. An index in an array corresponding to the current key is determined using a hash function. A previous key and a previous arrival time are retrieved from the array at the index. The array is transformed by replacing the previous key and the previous arrival time with the current key and the current arrival time in the array at the index. The previous key and the previous arrival time are inserted into a nearest eligible sequential index in the array.

Abstract: A current key is received at a current arrival time at a computer. An index in an array corresponding to the current key is determined using a hash function. A previous key and a previous arrival time are retrieved from the array at the index. The array is transformed by replacing the previous key and the previous arrival time with the current key and the current arrival time in the array at the index. The previous key and the previous arrival time are inserted into a nearest eligible sequential index in the array.

Abstract: A method for producing a summary A of data points in an unaggregated data stream wherein the data points are in the form of weighted keys (a, w) where a is a key and w is a weight, and the summary is a sample of k keys a with adjusted weights wa. A first reservoir L includes keys having adjusted weights which are additions of weights of individual data points of included keys and a second reservoir T includes keys having adjusted weights which are each equal to a threshold value ? whose value is adjusted based upon tests of new data points arriving in the data stream. The summary combines the keys and adjusted weights of the first reservoir L with the keys and adjusted weights of the second reservoir T to form the sample representing the data stream upon which further analysis may be performed.

Abstract: A method and apparatus for composite link assignment are provided such that network capacity is sufficient to handle all the traffic (e.g., load) while an objective function, e.g., the total cost of the capacity is minimized. The present method receives a plurality of weights for a plurality of arcs and a load for the network. An objective function is selected for minimization, where the present method then determines the composite link assignment to handle the load while the objective function is minimized. In one embodiment, the composite link assignment comprises a plurality of different link types for the plurality of arcs.

Abstract: Two regularized estimators that avoid the pathologies associated with variance estimation are disclosed. The regularized variance estimator adds a contribution to estimated variance representing the likely error, and hence ameliorates the pathologies of estimating small variances while at the same time allowing more reliable estimates to be balanced in the convex combination estimator. The bounded variance estimator employs an upper bound to the variance which avoids estimation pathologies when sampling probabilities are very small.

Abstract: The present invention relates to a method of obtaining a generic sample of an input stream. The method is designated as VAROPTk. The method comprises receiving an input stream of items arriving one at a time, and maintaining a sample S of items i. The sample S has a capacity for at most k items i. The sample S is filled with k items i. An nth item i is received. It is determined whether the nth item i should be included in sample S. If the nth item i is included in sample S, then a previously included item i is dropped from sample S. The determination is made based on weights of items without distinguishing between previously included items i and the nth item i. The determination is implemented thereby updating weights of items i in sample S. The method is repeated until no more items are received.

Abstract: Methods and apparatus to bound network traffic estimation error for multistage measurement sampling and aggregation are disclosed.

Abstract: A method for producing a summary A of data points in an unaggregated data stream wherein the data points are in the form of weighted keys (a, w) where a is a key and w is a weight, and the summary is a sample of k keys a with adjusted weights wa. A first reservoir L includes keys having adjusted weights which are additions of weights of individual data points of included keys and a second reservoir T includes keys having adjusted weights which are each equal to a threshold value ? whose value is adjusted based upon tests of new data points arriving in the data stream. The summary combines the keys and adjusted weights of the first reservoir L with the keys and adjusted weights of the second reservoir T to form the sample representing the data stream upon which further analysis may be performed.

Abstract: Disclosed herein are systems, methods, and computer-readable storage media for matching a regular expression in an input string. A system configured to practice the method first identifies a number of substrings (k) in a regular expression of length (m). The system receives a stream of start states for each of the substrings generated according to a regular expression matching process and receives a stream of end occurrences generated according to a multi-string matching process. The system identifies all instances where an end occurrence of a particular substring matches a positive start state of the particular substring, and enters the instances as positive substring accept states in the regular expression matching process on the input string. In one aspect, the system is much more efficient when (k) is much less than (m). The system can match the regular expression based on a bit offset between the first and second stream.

Abstract: A current key is received at a current arrival time at a computer. An index in an array corresponding to the current key is determined using a hash function. A previous key and a previous arrival time are retrieved from the array at the index. The array is transformed by replacing the previous key and the previous arrival time with the current key and the current arrival time in the array at the index. The previous key and the previous arrival time are inserted into a nearest eligible sequential index in the array.