A. V. Aho, J. E. Hopcroft, J. D. Ullman: The Design and Analysis of Computer Algorithms. Addison--Wesley, Reading, MA.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Of co. Thus the substring tree contains full suffixes of the tree, whereas the prefix tree only contains prefix identifiers. This makes the substring trees larger, both prefix trees and substring trees have a worst case size of O(n 2) nodes but prefix trees have an average size of O(n) Aho, Hopcroft Ullman 74] whereas substring trees only have an O(n) size in some special cases (e.g. an) But the algorithm for substring matching is simpler for the substring tree, since it just has to walk down the tree according to co t . It can also be noticed that the substring tree does not contain any ....

Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley (1974)

....associates the related information of s to s V. Once eq is deleted from Hs, it will not appear as a break point. Therefore the total number of deletions from the heap is O(n) Using efficient mergeable heaps such as the 2 3 tree, we are able to perform all these operations in O(n logn) time [1]. The algorithm for finding the nucleolus x is now described as follows. Algorithm Nucleolus Step 1: Apply Breaks(g) Step 2: Apply Nu rlow(r, u(N) Step 3: For each i C N, assign x f(ei) We now discuss the time complexity of this algorithm. The preprocess Breaks requires O(nlogn) ....

A. V. Aho, J. E. Hopcroft, and J. D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

....be updated with changes that are local to a path from the root to the leaf just inserted or deleted. So, the cost of updating the tree signature of the document is proportional to the height of the tree. The height of the tree is kept logarithmic in the number of leaves through the use of 2 3 tree [5]. From the security point of view, the tree signing algorithm achieves tamper proof security (see section 4 for more details) An open problem remains: the privacy of signatures. 1.1 The Privacy Problem The application that we have in mind is a text editor that maintains in the background ....

....text editor with incremental signature generation. When the final letter is complete, you certainly don t want the intermediate versions to be revealed through the signature. In this paper we solve this problem. We do this by introducing oblivious 2 3 trees, an implementation of 2 3 trees [5] in which the operations are defined as probabilistic algorithms and satisfy the intuitive property of hiding the sequence of operations that has been applied to a tree. 1.2 Oblivious 2 3 tree Our solution to the privacy problem consists of the definition of new insert and delete operations for ....

A. Aho, J. Hopcroft, J. Ullman The design and analysis of computer algorithms. Addison Wesley, 1974. 15

....(S, #, 0, 1) a right Kleene algebra (RKA) if (S, #, 0, 1) is a left Kleene algebra. A Kleene algebra (KA) cf. 4] is a quintuple (S, #, 0, 1) which is both an LKA and an RKA. In connection with graph algorithms, one often considers the related structure of a closed semiring (see e.g. [1]) It di#ers from a KA in that #K is only required to exist for countable K; moreover, idempotence of is not postulated. So every KA is a closed semiring, but not vice versa. Perhaps the best known example of a KA is LAN . #) the algebra of formal languages over some alphabet A, where ....

A.V. Aho, J.E. Hopcroft, J.D. Ullman: The design and analysis of computer algorithms. Reading, Mass.: Addison Wesley 1974

....computation model, NFA is a more useful tool for pattern matching. Simulation of NFA for pattern matching is a basic method for text searching. There are two basic method to construct NFA from regular expression. One is by Thompson, and the other is by McNaughton and Yamada(MY for short) In [1], they argued that working with an NFA without elimination of ffl transitions is far more efficient than working with an NFA after ffl reduction, although the new NFA has less states. But the MY s construction will be efficient in some special cases, one of these is all the occurrence of the ....

....the regular expression; and the number of states and transitions are linear w.r.t the number of alphabet character occurrences, which is not the case for the unimproved version of Thompson s construction. 1 2 1 Preliminaries A regular expression over an alphabet Sigma is defined as follows [1]: 1. ffl, OE and a for each a 2 Sigma are regular expressions denoting ffflg, the empty set and fag respectively; 2. If R 1 ; R 2 are regular expressions denoting the languages L 1 ; L 2 , respectively, then (R 1 R 2 ) R 1 R 2 ) and (R 1 ) are regular expressions, denoting L 1 [ L 2 , L 1 L ....

[Article contains additional citation context not shown here]

A. Aho, J. Hopocroft, J. Ullman The Design and Analysis of Computer Algorithms Addison-Wesley, Reading, Mass.

....both algorithms make use of the fact, that only full vertex covers are to be obtained. Therefore, when a vertex i is marked uncovered, all neighboring vertices can be covered immediately. Concerning these vertices, only the left subtrees are present in the search tree. The divide and conquer [33] approach is based on the fact that a minimum VC of a graph, which consists of several independent connected components, can be obtained by combining the minimum covers of the components. Thus, the full task can be split into several independent tasks. This strategy can be repeated at all levels ....

A.V. Aho, J.E. Hopcroft and J.D. Ullman: The design and analysis of computer algorithms, Addison-Wesley, Readin (MA) 1974

....i jf i j# with O# F # storage. The o# line min approach. If we can a#ord to sort the values F i by some method of distribution sort or radix sort, using O#n F # time or O#n log n F # time, respectively,we can then use the algorithm for the o# line min problem #cf. the three Americans book, Aho et al. 1974#. This leads to a very simple algorithm with a complexityofO#n##m; m##; where ##m; n# is the extremely slowly growing inverse function of the Ackermann function, cf. Tarjan and van Leeuwen #1984#. Using the improvement of Gabow and Tarjan #1985#, which makes the algorithm slightly more ....

A. V. Aho, J. E. Hopcroft, and J. D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

....lower bound for the time complexity of this method, where, n is the number of states. Note that in the worst case we need n refinement steps and in each refinement step we have to solve a linear equation system with n variables and n equations (which takes O(n 2. 8 ) time with the method of [2]) As a more e#cient alternative, we develop an algorithm that runs in time O(n 3 ) in the sequel. The basic idea is to replace ( by a condition that asserts that X violates the conditions of a branching bisimulation. To realise this idea, we use an alternative definition of a splitter that ....

A. Aho, J. Hopcroft, J. Ullman: The Design and Analysis of of Computer Algorithms, Addison-Wesley Publishing Company, 1974.

....proximity, it is essential to have an index over spatial locations. The underlying data structure must support efficient spatial operations, such as locating the neighbors of an object and identifying objects in a defined query region. Most indexes are based on the principle of divide and conquer [AHU74]. Indexing structures following this approach are typically hierarchical. The approach is naturally suitable for a database system where the memory space is limited, and hence the pruning of a search must be performed such that the more detail to be examined, the smaller number of objects are ....

A. V. Aho, J. E. Hopcroft, J. D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA (1974).

....modulo p. The total complexity is therefore O(Ld log(d)M(log(b) b= log(b) O(b 1 ffl L) The second Chinese remainder step involves a Chinese remainder computation on r primes of length O(log(b) for each of the L components. Using fast Chinese remaindering techniques as described in [1] or in [2] we obtain a running time of O(b 2 ffl L) O(b 1 ffl L log(L) for this step. At this stage of the algorithm we have obtained a vector of length L whose entries are integral linear combinations of powers of i with coefficients bounded by M in absolute value. For each of these ....

A.V. Aho, J.E. Hopcroft, and J.D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

....s ) s2V where b A s = P t2Sat( Phi 2 ) A(s; t) The computation of G A needs O(n 2 ) steps. As G A has at most n 2 edges, the test whether A is admissible takes O(n 2 ) steps. Solving a linear equation system with at most n variables and n equations can be done in time O(n 2:8 ) [6]. Thus, the computation of p adm s ( Phi 1 U Phi 2 ) takes O (jA admissible ( Phi 1 ; Phi 2 )j Delta n 2:8 ) time. Computation of T max ( Phi 1 ; Phi 2 ) and T adm ( Phi 1 ; Phi 2 ) We give an algorithm which returns T max ( Phi 1 ; Phi 2 ) The computation of T adm ( Phi 1 ; ....

A. Aho, J. Hopcroft, J. Ullman: The Design and Analysis of of Computer Algorithms, Addison-Wesley Publishing Company, 1974.

....the linear equation system (I Gamma A) Delta x = b. Here, I is the jV j Theta jV j identity matrix, A = A(s; v) s;v2V , b = b A s ) s2V , b A s = P t2Sat( Phi 2 ) A(s; t) Solving a linear equation system with at most n variables and n equations can be done in time O(n 2:8 ) [6]. Thus, the computation of p adm s ( Phi 1 U Phi 2 ) takes O Gamma jA adm ( Phi 1 ; Phi 2 )j Delta n 2:8 Delta time. Given an upper bound l for the number of transitions in every state (i.e. jSteps(s)j l for all s) we obtain jA adm ( Phi 1 ; Phi 2 )j l n . Hence, worst case ....

A. Aho, J. Hopcroft, J. Ullman: The Design and Analysis of of Computer Algorithms, Addison-Wesley Publishing Company, 1974.

....are regular expressions. The problem of finding minimal substrings matching a regular expression was described and solved in [1, Sect. 9.2. Our Algorithms A, B, AA and AB can be generalized even for regular expressions. In fact, the generalization of Algorithm B is exactly the solution given in [1]. Another related pattern matching problem is approximate string matching which looks for those substrings of the text T that can be transformed into the pattern P with at most k edit operations. When deletion is the only edit operation allowed and we choose k = w Gamma m, the problem is ....

....automatons for the pattern. 4 Algorithm B Our second algorithm for finding all minimal substrings is closely related to the basic dynamic programming algorithm for approximate string matching [8,9] The algorithm could also be derived from a minimal substring algorithm for regular expressions [1]. Essentially the same algorithm was also described in [6] and in more detail in [10] as a part of an algorithm for finding all frequent episodes. The algorithm computes a table S[0: n; 0: m] where S[i; j] is the largest value k such that T [k: i] contains P [1: j] Then, for every i and j such ....

[Article contains additional citation context not shown here]

A. V. Aho, J. E. Hopcroft and J. D. Ullman: The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.

....terms of exact security: Definition 2.2 (Security of Incremental Schemes) Let S(b; s) be an incremental signature or message authentication scheme with block size b and security parameter s. A (t; q s ; q v ; q i ; L s ; L v ; L i ; ffl) adversary E makes at most t steps (in a standard RAM model [AHU74] queries Sig, IncSig, Vf at most q s , q i , q v times, each query with messages of no more than L s , L i , L v blocks, and is successful with probability at least ffl. S(b; s) is said to be (t; q s ; q v ; q i ; L s ; L v ; L i ; ffl) secure against basic message substitution total ....

A.Aho, J.Hopcroft, J.Ullman: The Design and Analysis of Computer Algorithms, Addison Wesley, 1974.

.... involves a comparisonbased sort, which is O(n lg n) and RECTYPE normalization entails re encoding into a DFA (which can be done in linear time) followed by DFA minimization, which is O(ff n lg n) where ff is the size of the input alphabet [Aho Ullman 86, x3.9, pp.141 144] Hopcroft 71] Aho, Hopcroft Ullman 74, x4.13 Partitioning, pp.157 162] For our encoding, ff is the arity of the highest arity subexpression, which in practice can be assumed to be a constant probably less than about 8. 10 Of course, in general, some axioms may need to be reapplied in subsequent phases if some later (more ....

Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman The Design and Analysis of Computer Algorithms Addison-Wesley, 1974

....otherwise. Then the length of the shortest path between the nodes v i and v j is equal to the element c ij of matrix C = A n , where A n is computed on the basis of matrix multiplication, in which scalar multiplication has been replaced by addition and scalar addition by the minimum operation [1]. The implementation of the algorithm is given below. By successively computing A 2 , A 4 , we need only log 2 n iterations to compute A n (we assume for simplicity that n is a power of 2) void shpaths (int n) array unsigned a, b, c ; a = arraycreate (2, n,n 9 , 0,0, ....

....the skeleton arraymap. This applies the function copypivot to all elements of the array piv, overwriting only those, which correspond to the pivot row. The function copypivot is given below. t copypivot (array t b, int k, t v, Index ix) Bounds bds = arraypartbounds (b) if (bds lowerBd[1] = k k bds upperBd[1] return (arraygetelem (b, k,ix[1] arraygetelem (b, k,k) else return (v) Upon checking the arity of this function against its call in the gauss procedure and against the arity and type of the functional argument expected by the skeleton arraymap (see ....

[Article contains additional citation context not shown here]

A. V. Aho, J. E. Hopcroft, J. D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

No context found.

A. V. Aho, J. E. Hopcroft, J. D. Ullman: The Design and Analysis of Computer Algorithms. Addison--Wesley, Reading, MA.

No context found.

A. V. Aho, J. E. Hopcroft, J. D. Ullman: The Design and Analysis of Computer Algorithms. Addison--Wesley, Reading, MA.

No context found.

A. Aho, J. Hopcroft, J. Ullman: The Design and Analysis of of Computer Algorithms, Addison-Wesley Publishing Company, 1974.

No context found.

A.V. Aho, J.E. Hopcroft, J.D. Ullman: The Design and Analysis of Computer Algorithms, AddisonWesley 1974

No context found.

A. Aho, J. Hopcroft, and J. Ullman The Design and Analysis of Computer Algorithms. Addison-Wesley, 1972.

No context found.

A. Aho, J. Hopcroft, J. Ullman: The Design and Analysis of of Computer Algorithms, Addison-Wesley Publishing Company, 1974.

No context found.

A.Aho, J.Hopcroft, J.Ullman: The Design and Analysis of Computer Algorithms, Addison Wesley, 1974.

No context found.

A.V. Aho, J.E. Hopcroft, J.D. Ullman: The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1974.

No context found.

A.V. Aho, J.E. Hopcroft, J.D. Ullman: The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1974. Treats a number of classical algorithms and analyses their time and space complexity.

No context found.

A.V. Aho, J.E. Hopcroft, J.D. Ullman: The design and analysis of computer algorithms. Addison--Wesley 1974

No context found.

A. Aho, J. Hopcroft, J. Ullman: The Design and Analysis of of Computer Algorithms, Addison-Wesley Publishing Company, 1974.

No context found.

Aho, A. V., J. E. Hopcroft, and J. D. Ullman The Design and Analysis of Computer Algorithms. Addison Wesley, 1974.

No context found.

A.V. Aho, J. E. Hoprcroft, and J. D. Ullman The Design and Analysis of Computer Algorithms, London: Addison-Wesley (1974).

No context found.

Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley (1974)

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC