Proof of a conjecture on irredundance perfect graphs

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002     

Rank-perfect and" weakly rank-perfect graphs

An edge e of a perfect graph G is critical if G−e is imperfect. We would like to decide whether G−e is still “almost perfect” or already “very imperfect”. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.     

FFT-based algorithms for the string matching with mismatches problem

The string matching with mismatches problem requires finding the Hamming distance between a pattern P of length m and every length m substring of text T with length n. Fischer and Paterson's FFT-based algorithm solves the problem without error in O(σnlogm), where σ is the size of the alphabet Σ [SIAM–AMS Proc. 7 (1973) 113–125]. However, this in the worst case reduces to O(nmlogm). Atallah, Chyzak and Dumas used the idea of randomly mapping the letters of the alphabet to complex roots of unity to estimate the score vector in time O(nlogm) [Algorithmica 29 (2001) 468–486]. We show that the algorithm's score variance can be substantially lowered by using a bijective mapping, and specifically to zero in the case of binary and ternary alphabets. This result is extended via alphabet remappings to deterministically solve the string matching with mismatches problem with a constant factor of 2 improvement over Fischer–Paterson's method.     

Circular perfect graphs

For 1 ≤ d ≤ k, let K_k/d be the graph with vertices 0, 1, …, k ? 1, in which i ～j if d ≤ |i ? j| ≤ k ? d. The circular chromatic number χ_c(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to K_k/d. The circular clique number ω_c(G) of G is the maximum of those k/d for which K_k/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G, we have χ_c(H) = ω_c(H). In this paper, we prove that if G is circular perfect then for every vertex x of G, N_G[x] is a perfect graph. Conversely, we prove that if for every vertex x of G, N_G[x] is a perfect graph and G ? N[x] is a bipartite graph with no induced P₅ (the path with five vertices), then G is a circular perfect graph. In a companion paper, we apply the main result of this paper to prove an analog of Haj?os theorem for circular chromatic number for k/d ≥ 3. Namely, we shall design a few graph operations and prove that for any k/d ≥ 3, starting from the graph K_k/d, one can construct all graphs of circular chromatic number at least k/d by repeatedly applying these graph operations. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 186–209, 2005     

Bit-parallel approximate string matching algorithms with transposition

Using bit-parallelism has resulted in fast and practical algorithms for approximate string matching under Levenshtein edit distance, which permits a single edit operation to insert, delete or substitute a character. Depending on the parameters of the search, currently the fastest non-filtering algorithms in practice are the O(km/wn) algorithm of Wu and Manber, the O((k+2)(m−k)/wn) algorithm of Baeza-Yates and Navarro, and the O(m/wn) algorithm of Myers, where m is the pattern length, n is the text length, k is the error threshold and w is the computer word size. In this paper we discuss a uniform way of modifying each of these algorithms to permit also a fourth type of edit operation: transposing two adjacent characters in the pattern. This type of edit distance is also known as Damerau edit distance. In the end we also present an experimental comparison of the resulting algorithms.     

匹配问题实例空间和解空间结构

本文通过研究匹配问题的实例空间，匈牙利算法和解空间三者之间的关系，指出S实例空间的数目与问题复杂度之间的关系既不是充分也不是必要的，而如何对问题的解空间进行合理的分解才能是问题的关键。     

Fold‐2‐covering triangular embeddings

For a graph G and a positive integer m, G_(m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m² edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G_(m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G_(m) does triangulate a surface, and in fact does so as a “covering with folds” of the original triangulation. For m = 5, this would be a consequence of Tutte's 5‐Flow Conjecture. In this work, we investigate the case m = 2 and describe simple classes of triangulations G for which G₍₂₎ does have a triangulation that covers G “with folds,” as well as providing a simple infinite class of triangulations G of the sphere for which G₍₂₎ does not triangulate any surface. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 79–92, 2003     

Chern and Pontryagin Numbers in Perfect Symmetries of Spheres

The paper presents a procedure for constructing smooth actions of finite perfect groups on spheres with fixed point sets having certain prescribed properties (Theorem A); in particular, having any prescribed configuration of Chern and Pontryagin numbers (Corollary C). The main ingredients used are equivariant thickening and equivariant surgery.     

磁拱的运动学无力场

本文首先推导了完全导电流体内运动学磁拱无力场的基本方程，接着考虑了静态解和不定常相似性解．     

全固态多波长飞秒脉冲激光系统

利用棱镜对引进频谱空间啁啾来补偿飞秒脉冲激光二次谐波产生中的相位失配,提高了倍频效率建立了一套全固态、多波长(1065nm, 532nm,823.1nm, 402nm)飞秒脉冲激光系统自制的Nd:YVO4激光器输出532nm绿光激光,最高平均功率可达5.6W当用2.5W绿光激光泵浦时,从自制的钛宝石激光器及经BBO倍频可分别输出中心波长为823.1nm和402nm,平均功率300mW和73mW,谱宽32.3nm和5.1nm,脉宽22fs和33.3fs、重复率108MHz的近红外和蓝光激光整个系统具有结构紧凑、倍频效率高、运行稳定的特点.