207081381
Enumeration of Regular Graph Coverings Having Finite Abelian Covering Transformation Groups
Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors. An enumeration of the isomorphism classes of n-fold coverings of a graph G was done by Kwak and Lee [Canad. J. Math., XLII (1990), pp. 747--761] and independently by Hofmeister [Discrete Math., 98 (1991), pp. 437--444]. An enumeration of the isomorphism classes of connected n-fold coverings of a graph G was recently done by Kwak and Lee [J. Graph Theory, 23 (1996), pp. 105--109]. But the enumeration of the isomorphism classes of regular coverings of a graph G has been done for only a few cases. In fact, the isomorphism classes of ${\cal A}$-coverings of G were enumerated when ${\cal A}$ is the cyclic group $\BZ_n$, the dihedral group $\BD_n$ (n: odd), and the direct sum of $m$ copies of $\BZ_p$. (See [Discrete Math., 143 (1995), pp. 87--97], [J. Graph Theory, 15 (1993), pp. 621--627], and [Discrete Math., 148 (1996), pp. 85--105]). 
In this paper, we discuss a method to enumerate the isomorphism classes of connected ${\cal A}$-coverings of a graph G for any finite group ${\cal A}$ and derive some formulas for enumerating the isomorphism classes of regular n-fold coverings for any natural number n. In particular, we calculate the number of the isomorphism classes of ${\cal A}$-coverings of G when ${\cal A}$ is a finite abelian group or the dihedral group $\BD_n$. Our method gives partial answers to the open problems 1 and 2 in [Discrete Math., 148 (1996), pp. 85--105] and also gives a formula to calculate the number of the subgroups of a given index of any finitely generated free abelian group.
40285902
Isoperimetric numbers and bisection widths of double coverings of a complete graph
16002222
Isomorphism classes of cycle permutation graphs
Abstract In this paper, we construct a cycle permutation graph as a covering graph over the dumbbell graph, and give a new characterization of when two given cycle permutation graphs are isomorphic by a positive or a negative natural isomorphism. Also, we count the isomorphism classes of cycle permutation graphs up to positive natural isomorphism, and find the number of distinct cycle permutation graphs isomorphic to a given cycle permutation graph by a positive/negative natural isomorphism. As a consequence, we obtain a formula for finding the number of double cosets of the dihedral group in the symmetric group.
623251
Isomorphism classes of bipartite cycle permutation graphs
43495365
A scalable cache coherent architecture for large-scale mesh-connected multiprocessors
Until now, various limited directory-based cache coherence protocols were proposed for medium- or large-scale multiprocessors while employing scalable directory memories. For widely shared data, however, most protocols suffer from extraneous cache invalidates or updates due to insufficient pointers. We focus on large-scale mesh-connected multiprocessors built on top of wormhole and dimension ordered routing networks. In such networks, worms are major bricks for communications, which transit all the intermediate nodes on their way to a destination. From such an observation, we propose a new directory-based protocol DirQ with limited pointers, which can represent either one node or a set of nodes when being widely shared. For /spl radic/N/spl times//spl radic/N processors system, our protocol needs /spl Theta/(N/sup 3/2/ log N) bits for directory memory which is much more scalable compared to the full-map protocol. In terms of latency and traffic volume for cache coherence, our analytic models show that DirQ outperforms other limited protocols, and further comparable to the full-map one.
3426940
n-Gram/2L: A Space and Time Efficient Two-Level n-Gram Inverted Index Structure
The n-gram inverted index has two major advantages: language-neutral and error-tolerant. Due to these advantages, it has been widely used in information retrieval or in similar sequence matching for DNA and protein databases. Nevertheless, the n-gram inverted index also has drawbacks: the size tends to be very large, and the performance of queries tends to be bad. In this paper, we propose the two-level n-gram inverted index (simply, the n-gram/2L index) that significantly reduces the size and improves the query performance while preserving the advantages of the n-gram inverted index. The proposed index eliminates the redundancy of the position information that exists in the n-gram inverted index. The proposed index is constructed in two steps: 1) extracting subsequences of length m from documents and 2) extracting n-grams from those subsequences. We formally prove that this two-step construction is identical to the relational normalization process that removes the redundancy caused by a non-trivial multivalued dependency. The n-gram/2L index has excellent properties: 1) it significantly reduces the size and improves the performance compared with the n-gram inverted index with these improvements becoming more marked as the database size gets larger; 2) the query processing time increases only very slightly as the query length gets longer. Experimental results using databases of 1 GBytes show that the size of the n-gram/2L index is reduced by up to 1.9 ~ 2.7 times and, at the same time, the query performance is improved by up to 13.1 times compared with those of the n-gram inverted index.
47092701
Loop formulas for circumscription
Clark's completion is a simple nonmonotonic formalism and a special case of many nonmonotonic logics. Recently there has been work on extending completion with "loop formulas" so that general cases of nonmonotonic logics such as logic programs (under the answer set semantics) and McCain-Turner causal logic can be characterized by propositional logic in the form of "comple(ion + loop formulas". In this paper, we show that the idea is applicable to McCarthy's circumscription in the propositional case. We also show how to embed propositional circumscription in logic programs and in causal logic, inspired by the uniform characterization of "completion + loop formulas".
19081367
Robust technique for estimating the bearings of cyclostationary signals
This paper deals with the problem of direction finding using cyclostationary signals in the presence of cycle frequency error (CFE). By exploiting the signal cyclostationarity, cyclic MUSIC and conjugate cyclic MUSIC presented in Gardner (Cyclostationarity in Communications and Signal Processing, New York, 1994; Proc. IEEE 76 (1988) 845) have been shown to be effective for signal-selective direction finding. However, they suffer from severe performance degradation even if there is a small error in the cycle frequency of the signals of interest. In this paper, we first evaluate the performance of conjugate cyclic MUSIC when CFE exists. An analytical formula is derived to show the behavior of the performance degradation due to CFE. By exploiting the eigenstructure of the conjugate cyclic correlation matrix of the received array data, we develop a technique including a method for estimating the cycle frequency of the SOI and an efficient method in conjunction with a subspace-fitting algorithm to achieve robust direction finding against CFE. Several simulation examples confirming the theoretical analysis and showing the effectiveness of the proposed technique are also presented.
18632465
Automatic Recovery from Disk Failure in Continuous-Media Servers
Continuous-media (CM) servers have been around for some years. Apart from server capacity, another important issue in the deployment of CM servers is reliability. This study investigates rebuild algorithms for automatically rebuilding data stored in a failed disk into a spare disk. Specifically, a block-based rebuild algorithm is studied with the rebuild time and buffer requirement modeled. A buffer-sharing scheme is then proposed to eliminate the additional buffers needed by the rebuild process. To further improve rebuild performance, a track-based rebuild algorithm that rebuilds lost data in tracks is proposed and analyzed. Results show that track-based rebuild, while it substantially outperforms block-based rebuild, requires significantly more buffers (17-135 percent more) even with buffer sharing. To tackle this problem, a novel pipelined rebuild algorithm is proposed to take advantage of the sequential property of track retrievals to pipeline the reading and writing processes. This pipelined rebuild algorithm achieves the same rebuild performance as track-based rebuild, but reduces the extra buffer requirement to insignificant levels (0.7-1.9 percent). Numerical results computed using models of five commercial disk drives demonstrate that automatic rebuild of a failed disk can be done in a reasonable amount of time, even at relatively high server utilization (e.g., less than 1.5 hours at 90 percent utilization).