Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....B) is an arc of F if and only if there is a non edge between B and B 0 . We nd the strongly connected components of F , and the component graph, which has one node for each strong component of F , and arcs telling which strongly connected components are reachable from which on a single arc of F (Cormen et al. 1990)) A topological sort gives the chain of ancestors of v 0 , by giving the sets of nodes that must be added to an ancestor to get its parent. The proof is given below. Figure 8 gives an example. e,h,i,j, q a,b,c d f,g a,b,c h,i,j, q f,g e d Forcing graph Adjacencies ....

....time, by concatenating all adjacency lists and then radix sorting the resulting list using vertex of origin as primary sort key and ending vertex as secondary sort key. This is accomplished with two stable O(n m) sorts, a rst one on the secondary key and a second 12 one on the primary key, see Cormen et al. 1990). We obtain the adjacency lists by cutting this nal list at points where the primary sort key changes. 4.0.3 Union Find We need a Union Find data structure for some of our operations. This is any structure that maintains a partition P of a set V , and supports the following operations: ....

[Article contains additional citation context not shown here]

Cormen, T. H., Leiserson, C. E., and Rivest, R. L. (1990). Algorithms. MIT Press, Cambridge, Massachusetts.

....of a digraph is an ordering of its vertices so that every arc goes from an earlier to a later vertex in that ordering. A digraph has a topological sort i it is a dag, and, ordering the vertices of a dag in descending order of nishing time in any depth rst search gives a topological sort, see Cormen et al. 1990). Thus, we may nd a topological sort of any dag in G s outward class in O(n(G) m(G) time. RR n 3832 16 Elias Dahlhaus, Jens Gustedt, Ross M. McConnell 8 Longest path in a dag We will let the length of a path denote the number of arcs in it. The length of the longest path in a digraph is ....

....the component graph G=P is a dag. The component graph tells which components have a path to which. Below, we will nd it useful to compute not just the strongly connected components of a member of G s outward equivalence class, but a topological sort of its component graph. An algorithm given in Cormen et al. 1990) for strongly connected components also produces a topological sort of the component graph, though this is not mentioned explicitly. Most people who are familiar with the proof of that algorithm would have little trouble establishing this, but for completeness, we give a proof here. Let us de ne ....

Cormen, T. H., Leiserson, C. E., and Rivest, R. L. (1990). Algorithms. MIT Press, Cambridge, Massachusetts.

.... m) time, by concatenating all adjacency lists and then radix sorting the resulting list using vertex of origin as primary sort key and ending vertex as secondary sort key. This is accomplished with two stable O(n m) sorts, a rst one on the secondary key and a second one on the primary key, see Cormen et al. 1990). We obtain the adjacency lists by cutting this nal list at points where the primary sort key changes. RR n 3804 8 Elias Dahlhaus, Jens Gustedt, Ross M. McConnell 2.2.3 Union Find We need a Union Find data structure for some of our operations. This is any structure that maintains a partition P ....

....v 2 V . Union : Given v; w 2 V , merge the the two sets of P that contain v and w by replacing them with their union in P. An arbitrary sequence starting with one Initialize, on a set of size n, and a mixed sequence of n 1 Union and m Find operations takes O(n (m;n) time, see Tarjan (1983) Cormen et al. 1990). The is an extremely slow growing but unbounded function that has value at most four in any practical application of the data structure. To achieve a linear time bound for modular decomposition, a certain restriction of the union nd problem will be relevant. We say that a sequence of Union ....

[Article contains additional citation context not shown here]

Cormen, T. H., Leiserson, C. E., and Rivest, R. L. (1990). Algorithms. MIT Press, Cambridge, Massachusetts.

....consecutive symbols. Any non consecutive subset will have a convex hull that contains a character which is not in the set. The algorithms necessary for computing with convex hulls are very efficient. A convex hull of a point set can be computed in O(nlogn) where n is the number of points (Cormen, Leiserson, Rivest 1991). Computing the convex hull union of two convex hulls is O(m l) where l and m are the number of vertices in the convex hulls. The intersection of two convex hulls can be found in O(m l) also. Unfortunately it is possible to construct an artificial arrangement of two dimensional symbols for ....

Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. 1991.

....the state independent decoding property. The extension of the method of poles to the case of sofic constraints is described in Section 4. In this paper, we shall sometimes describe algorithms as programs written in a pseudo code that is very much like C or Pascal. We adopt the conventions given in [12], page 4. 2 Definitions and background Let A be an alphabet, that is, a finite set of symbols called letters. A finite state automaton A = Q; E) on the alphabet A is composed of two finite sets: Q, the set of states, and E, the set of edges. The set of edges is included in Q Theta A Theta Q. A ....

Cormen, T., Leiserson, C., and Rivest, R. Algorithms. MIT Press, McGraw Hill, 1990.

....post ) EUmax (M post ) includes all utility values in the set corresponding to post ; this interval is therefore an approximation of the expected utility of plan p. The following theorem shows that it is easy to compute EUmax and EUmin for IMAs, using the fractional knapsack greedy algorithm (Cormen, Leiserson, Rivest 1990). Theorem 2 For an IMA M with n branches hI i ; B i i let U max;i = max b 2 B i U (b) and U min;i = min b 2 B i U (b) i = 1; 2; Delta Delta Delta ; n. We have EUmax (M ) max P i p i =1;p i 2I i X i p i Delta U max;i (4) EUmin (M ) min P i p i =1;p i 2I i X i p i Delta ....

....with n branches hI i ; B i i let U max;i = max b 2 B i U (b) and U min;i = min b 2 B i U (b) i = 1; 2; Delta Delta Delta ; n. We have EUmax (M ) max P i p i =1;p i 2I i X i p i Delta U max;i (4) EUmin (M ) min P i p i =1;p i 2I i X i p i Delta U min;i : 5) According to (Cormen, Leiserson, Rivest 1990), the greedy algorithm to compute EUmax (M ) and EUmin (M ) runs in O(n log n) time. An Implementation Projection Rule 1 provides an algorithm to project plans, but if it is to be used efficiently in practice, computing the terms M i(B c i ) in (3) must be done in an effective way. Similarly, ....

Cormen, T.; Leiserson, C. E.; and Rivest, R. L. 1990.

....To prevent duplicate entries, we need to check if an equivalent node is already present in the DAG, when inserting a node. To achieve this, we can store the nodes in a data structure on which an efficient search operation is defined, such as a hash table (as in Handley (1994) or a red black tree (Cormen, Leiserson, and Rivest (1990)) A red black tree is less time efficient, using O(log n) time per insertion, in comparison to a hash table, which is O(1) but this is of secondary importance, since time performance in genetic programming is, in most cases, dominated by evaluation time. The red black tree does lack ....

Cormen, T.H., Leiserson, C.E. and Rivest, R.L. 1990.

.... = #) # (#3 = 2) #2 # 0) # (#3=2) # (#1 = #) #1 = # A1 A2 A3 A 1 2 B 1 2 Z 0 2 A1 A2 A3 A 1 2 B 1 2 Z 0 2 Figure 1: An Simplified Example Learning Scenario If the proposed rule has more than one antecedent literal, such as rule (1) then the system can use the greedy minimum set cover algorithm (Cormen, Leiserson, Rivest 1989) to eliminate unnecessary constraints. The problem of minimum set cover is to find a subset from a given collection of sets such that the union of the sets in the subset is equal to the union of all sets. We rewrite rule (1) as (5) A1 = Z 0 ) A2 0) A3 = 2) The problem of compressing ....

Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. (1989).

....= NH ; EH ) iii) a function of final reward P X i 2V r i X i , and (iv) the initial values of the variables in V . Output: An optimal policy for the plan. 1. Identify the coherent fragments and derive the fragment graph from the high level plan H by finding strongly connected components in H [1]. 2. Identify (i) the sets of active variables for coherent fragments, ii) the sets of terminal variables, starting variables, and coupling variables among coherent fragments by scanning through the plan steps in H. 3. Repeat Step 4 and Step 5 until all coherent fragments are processed. 4. Pick ....

Corman, T. H., Leiserson, C. E., and Rivest, R. L., Algorithms, (MIT Press, Cambridge, Massachusetts, 1991).

....log PD (x i ;x j ) PD (x i ) PD (x j ) between each pair of variables, i 6= j. 2. Build a complete undirected graph in which the vertices are the variables in U. Annotate the weight of an edge connecting X i to X j by I(X i ; X j ) 3. Build a maximum weighted spanning tree of this graph (Cormen, Leiserson, Rivest 1990). 7 These structures are called Bayesian conditional trees by Geiger. 1 9 4 6 2 11152219 7 1810 8 211714 3 1316 5 1220 0.1 0.2 0.3 0.4 Error Figure 4: Error curves comparing smoothed TAN (solid line) to naive Bayes (dashed line) 3 21 5 1 7 6 8 20191815 9 17 2 10221611141312 4 0.05 0.1 0.15 ....

Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. 1990.

.... of similarity that we use is Dynamic Time Warping (DTW) Sankoff Kruskall 1 For more information on the algorithm for finding distinctive subsequences see (Oates 1999) 1983) DTW is a generalization of classical algorithms for comparing discrete sequences (e.g. minimum string edit distance (Cormen, Leiserson, Rivest 1990)) to sequences of continuous values. It was used extensively in speech recognition, a domain in which the time series are notoriously complex and noisy, until the advent of Hidden Markov Models, which offered a unified probabilistic framework for the entire recognition process (Jelinek 1997) ....

Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. 1990.

....optimum and its likelihood is used as the fitness. With this approach, one skips from a local optimum to another throughout the crossover and mutation operators. Finally, CAR T H AGENE maintains a set of fixed size containing the S best different maps encountered during the search. A hash table (Cormen, Leiserson, Rivest 1990) is used to efficiently test if the map is already present in the set, a heap structure is used to efficiently manage insertions deletions (Cormen, Leiserson, Rivest 1990) At the end of the search, the user can browse this set and check for the existence of other maps whose likelihood is close ....

....T H AGENE maintains a set of fixed size containing the S best different maps encountered during the search. A hash table (Cormen, Leiserson, Rivest 1990) is used to efficiently test if the map is already present in the set, a heap structure is used to efficiently manage insertions deletions (Cormen, Leiserson, Rivest 1990). At the end of the search, the user can browse this set and check for the existence of other maps whose likelihood is close to the best map s likelihood in order to get an idea of how strongly the best map is supported. Missing Data and Joined Maps We have seen that two points and multipoint ....

Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. 1990.

No context found.

Cormen, T. H.; Leiserson, C. E.; and Rivest, R. L. 1990.

No context found.

Cormen, Thomas H., Leierson, Charles E., and Rivest, Ronald L., #### ######## ## ##########, pp.465-472, The MIT Press, 2000.

No context found.

Cormen, T., Leiserson, C., and Rivest, R. Algorithms. MIT Press, McGraw Hill, 1990.

No context found.

Cormen, Leiserson, and Rivest. Algorithms. MIT Press and McGraw-Hill, 1994.

No context found.

Cormen, T. H., Leiserson, C. E., and Rivest, R. L., Heapsort, in Introduction to Algorithms, MIT Press, Cambridge, Mass., 140#152, 1990.

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