In this paper, we study the net adding problem arising in VLSI layout process. Given a layout H and a new net N, we attempt to add net N to layout H without changing H. We present an efficient method to find a solutio...
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In this paper, we study the net adding problem arising in VLSI layout process. Given a layout H and a new net N, we attempt to add net N to layout H without changing H. We present an efficient method to find a solution or report there is no solution to the given problem. Our solution is optimal in minimizing the number of vias required in two-terminal cases, and nearly optimal in multi-terminal cases.
Let G = (V, E) be an undirected graph with m edges and n vertices such that each edge e has a real valued weight w(e). Let MST(G) be a minimum spanning tree in G. Let f(G) be the weight of a minimum spanning tree of G...
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Let G = (V, E) be an undirected graph with m edges and n vertices such that each edge e has a real valued weight w(e). Let MST(G) be a minimum spanning tree in G. Let f(G) be the weight of a minimum spanning tree of G if G is connected;otherwise f(G) = infinity. We define a most vital edge with respect to a minimum spanning tree in a connected undirected graph G as an edge e such that f(G - e) greater-than-or-equal-to f(G - e') for every edge e' in G. In this paper, we give O(m + n log n) and O(ma(m, n)) time algorithms, which improve O(m log m) and O(n2) time bounds by Hsu et al. in Inform. Process. Lett. 39 (1991) 277-281.
We present a new linear algorithm for coloring the edges of a tree. Although this is not the first linear algorithm for the problem, our algorithm unlike the existing ones can be parallelized directly. The paralleliza...
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We present a new linear algorithm for coloring the edges of a tree. Although this is not the first linear algorithm for the problem, our algorithm unlike the existing ones can be parallelized directly. The parallelization is obtained by showing that edge-coloring can be carried out using tree contraction. Hence, it can be done in O(log n) time using n/log n processors on the EREW PRAM. When the problem is extended to one of coloring the edges of a graph with edge-disjoint cycles, the said algorithm for trees can be extended very easily without increasing the resource requirement.
Multiple sequence alignment is an important problem in computational molecular biology. Dynamic programming for optimal multiple alignment requires too much time to be practical. Although many algorithms for suboptima...
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Multiple sequence alignment is an important problem in computational molecular biology. Dynamic programming for optimal multiple alignment requires too much time to be practical. Although many algorithms for suboptimal alignment have been suggested, no "performance guarantees" algorithms have been known until recently. A computationally efficient approximation multiple alignment algorithm with guaranteed error bounds equal to the normalized communication cost of a corresponding graph is given in this paper. Recently, Altschul and Lipman [SIAM J. Appl. Math., 49 (1989), pp. 197-2091 used suboptimal alignments for reducing the computational complexity of the optimal alignment algorithm. This paper develops the Altschul-Lipman approach and demonstrates that bounds for optimal multiple alignment of k sequences can be derived from a solution of the maximum weighted matching problem in a k-vertex graph. Fast maximum matching algorithms allow efficient implementation of dynamic bounds for the multiple alignment problem.
In this paper we study subtree isomorphism and its relationships with some important symbolic problems. Recently, a linear time algorithm for ordered subtree isomorphism was given by Makinen. We note that a subtree of...
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In this paper we study subtree isomorphism and its relationships with some important symbolic problems. Recently, a linear time algorithm for ordered subtree isomorphism was given by Makinen. We note that a subtree of a rooted tree T, in Makinen's paper, refers to the tree rooted at any vertex in T. We consider ordered subtree isomorphism when a broader definition of subtree is used, viz., a subtree of T is any connected subgraph, including upsilon, of the tree rooted at any vertex-upsilon in T. We give some evidence to show that a linear time algorithm for this problem is unlikely. We also give an almost linear time reduction from the important problem of pattern matching to ordered subtree isomorphism. Finally, we present simpler linear time algorithms for ordered and unordered subtree isomorphism (with the more restrictive definition of subtree).
A complete characterization of the class of graphs that admit a cylindric visibility representation is presented, where vertices are represented by intervals parallel to the axis of the cylinder and the edges correspo...
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A complete characterization of the class of graphs that admit a cylindric visibility representation is presented, where vertices are represented by intervals parallel to the axis of the cylinder and the edges correspond to pairs of visible intervals. Moreover, linear time algorithms are given for testing the existence of and constructing such a representation. Important applications of cylindric visibility representations can be found in the layout of regular VLSI circuits, such as linear systolic arrays and bit-slice architectures. Also, alternative "dual" characterizations are presented of the graphs that admit visibility representations in the plane and in the cylinder. It is interesting to observe that neither of these two classes is contained in the other, although they have a nonempty intersection.
This paper re-examines, in a unified framework, two classic approaches to the problem of finding a longest common subsequence (LCS) of two strings, and proposes faster implementations for both. Letl be the length of a...
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This paper re-examines, in a unified framework, two classic approaches to the problem of finding a longest common subsequence (LCS) of two strings, and proposes faster implementations for both. Letl be the length of an LCS between two strings of lengthm andn ≥m, respectively, and let s be the alphabet size. The first revised strategy follows the paradigm of a previousO(ln) time algorithm by Hirschberg. The new version can be implemented in timeO(lm · min logs, logm, log(2n/m)), which is profitable when the input strings differ considerably in size (a looser bound for both versions isO(mn)). The second strategy improves on the Hunt-Szymanski algorithm. This latter takes timeO((r +n) logn), wherer≤mn is the total number of matches between the two input strings. Such a performance is quite good (O(n logn)) whenr∼n, but it degrades to Θ(mn logn) in the worst case. On the other hand the variation presented here is never worse than linear-time in the productmn. The exact time bound derived for this second algorithm isO(m logn +d log(2mn/d)), whered ≤r is the number ofdominant matches (elsewhere referred to asminimal candidates) between the two strings. Both algorithms require anO(n logs) preprocessing that is nearly standard for the LCS problem, and they make use of simple and handy auxiliary data structures.
Two parallel algorithms for finding the lowest common ancestors of a set of vertex pairs Q (the query set) in a directed tree are presented. With all the overheads taken into account, these algorithms take O((n + QI) ...
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Two parallel algorithms for finding the lowest common ancestors of a set of vertex pairs Q (the query set) in a directed tree are presented. With all the overheads taken into account, these algorithms take O((n + QI) P log2 n) and O(n2/p + log2n) time, respectively, with p(> 0) processors (n is the size of the tree). These results are better than the best known result in that the first achieves th
A variety of data structures such as inverted file, multi-lists, quad tree, k-d tree, range tree, polygon tree, quintary tree, multidimensional tries, segment tree, doubly chained tree, the grid file, d -fold tree. su...
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A variety of data structures such as inverted file, multi-lists, quad tree, k-d tree, range tree, polygon tree, quintary tree, multidimensional tries, segment tree, doubly chained tree, the grid file, d -fold tree. super B -tree, Multiple Attribute Tree (MAT), etc. have been studied for multidimensional searching and related problems. Physical data base organization, which is an important application of multidimensional searching, is traditionally and mostly handled by employing inverted file. This study proposes MAT data structure for bibliographic file systems, by illustrating the superiority of MAT data structure over inverted file. Both the methods are compared in terms of preprocessing, storage and query costs. Worst-case complexity analysis of both the methods, for a partial match query, is carried out in two cases: (a) when directory resides in main memory, (b) when directory resides in secondary memory. In both cases, MAT data structure is shown to be more efficient than the inverted file method. Arguments are given to illustrate the superiority of MAT data structure in an average case also. An efficient adaptation of MAT data structure, that exploits the special features of MAT structure and bibliographic files, is proposed for bibliographic file systems. In this adaptation, suitable techniques for fixing and ranking of the attributes for MAT data structure are proposed. Conclusions and proposals for future research are presented.
This paper contains the synthesis of three well-known scheduling algorithms starting from a common high level definition. The scheduling algorithms have been synthesised using program transformation techniques.
This paper contains the synthesis of three well-known scheduling algorithms starting from a common high level definition. The scheduling algorithms have been synthesised using program transformation techniques.
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