A homogeneous set is a non-trivial module of a graph, i.e., a non-unitary, proper subset H of a graph's vertices such that all vertices in H have the same neighbors outside H. Given two graphs G(1)(V, E-1), G(2)(V...
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A homogeneous set is a non-trivial module of a graph, i.e., a non-unitary, proper subset H of a graph's vertices such that all vertices in H have the same neighbors outside H. Given two graphs G(1)(V, E-1), G(2)(V, E-2), the Homogeneous Set Sandwich Problem asks whether there exists a sandwich graph G(S)(V, E-S), E-1 subset of or equal to E-S subset of or equal to E-2, which has a homogeneous set. Recently, Tang et al. [Inform. Process. Lett. 77 (2001) 17-22] proposed an interesting O(Delta(1) (.) n(2)) algorithm for this problem, which has been considered its most efficient algorithm since. We show the incorrectness of their algorithm by presenting three counterexamples. (C) 2004 Elsevier B.V. All rights reserved.
Efficient dynamic algorithms are presented for 4 geometric intersection problems: 1. reporting the subset of a set of nonintersecting segments in a plane that are intersected by a query segment of fixed slope, 2. re...
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Efficient dynamic algorithms are presented for 4 geometric intersection problems: 1. reporting the subset of a set of nonintersecting segments in a plane that are intersected by a query segment of fixed slope, 2. reporting the segments in a set of nonintersecting segments that are intersected by a query segment whose supporting line passes through a fixed point, 3. the orthogonal segment intersection search problem, and 4. the point enclosure problem for isothetic hyper-rectangles in d-dimensional spaces, where d is greater than or equal to 2. The algorithms are the first linear-space solutions for the first 3 problems and for the 4th problem in the plane. The update time for the 3rd problem has been improved over the previous best by a logarithmic factor without affecting the query time. For the 4th problem, the update time either matches or improves upon the previous best algorithms, but the query time is greater by a logarithmic factor. The first 2 problems previously had no known dynamic algorithms.
This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, a...
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This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, and adding at most k edges, where i,j, k are fixed integers. It is shown that this problem is fixed-parameter tractable whenever the hereditary property can be characterized by a finite set of forbidden induced subgraphs. Furthermore, the problem of deciding whether a graph can be made into a chordal graph by adding a fixed number k of edges is shown to be solvable in O(4(k)(k + 1)(-3/2)(m + n)) time, and is thus fixed-parameter tractable.
A new algorithm based on the Wu-Manber algorithm for multiple string matching is presented in this paper. The algorithm eliminates the functional overlap of the table HASH and SHIFT, and computes the shift distances i...
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A new algorithm based on the Wu-Manber algorithm for multiple string matching is presented in this paper. The algorithm eliminates the functional overlap of the table HASH and SHIFT, and computes the shift distances in an aggressive manner. After each test, the algorithm examines the character next to the scan window to maximize the shift distance. This idea is consistent with that of the quick-search (QS) algorithm. Experimental results on four alphabets show that the new algorithm is more efficient than Wu-Manber and other recent algorithms, particularly on short pattern sets and large alphabet. (C) 2009 Elsevier B.V. All rights reserved.
Assuming that nodes in a complete communication network fail with constant probability p < 1, individual calls fail with constant probability q < 1 and all failures are independent, we give an algorithm which br...
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Assuming that nodes in a complete communication network fail with constant probability p < 1, individual calls fail with constant probability q < 1 and all failures are independent, we give an algorithm which broadcasts information from a given fault-free node to all other fault-free nodes, with probability converging to 1, as the number of nodes grows. The algorithm works in expected logarithmic time.
We present a new simple algorithm that constructs an Aho Corasick automaton for a set of patterns, P, of total length n, in O(n) time and space for integer alphabets. Processing a text of size m over an alphabet Sigma...
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We present a new simple algorithm that constructs an Aho Corasick automaton for a set of patterns, P, of total length n, in O(n) time and space for integer alphabets. Processing a text of size m over an alphabet Sigma with the automaton costs O(m log |Sigma| + k), where there are k occurrences of patterns in the text. A new, efficient implementation of nodes in the Aho Corasick automaton is introduced, which works for suffix trees as well. (c) 2005 Elsevier B.V. All rights reserved.
String matching is the problem of finding all the occurrences of a pattern in a text. We propose a very fast new family of string matching algorithms based on hashing q-grams. The new algorithms are the fastest on man...
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String matching is the problem of finding all the occurrences of a pattern in a text. We propose a very fast new family of string matching algorithms based on hashing q-grams. The new algorithms are the fastest on many cases, in particular, on small size alphabets. (c) 2007 Elsevier B.V. All rights reserved.
We present an algorithm for constructing a perfect word hash function for n integers that takes O (n(4) logn) time. This time is independent of size of the integers or the number of bits in the integers. We call it a ...
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We present an algorithm for constructing a perfect word hash function for n integers that takes O (n(4) logn) time. This time is independent of size of the integers or the number of bits in the integers. We call it a word hash function because we require that the hash function can hash multiple integers packed in a word in constant time. Previous algorithms for constructing a perfect word hash function have time dependent on the number of the bits in integers. Although an O (n(loglogn)(2)) time algorithm is known for constructing a perfect hash function, the hash function constructed is not a word hash function and it cannot hash multiple integers packed in one word in constant time. The property of word hashing is indispensable in the current best deterministic and randomized algorithms for integer sorting. Our result is achieved via an algorithm of O (n(2) log(2) n) time that computes the shift distances for integers of St (n(2) log ri) bits. These shift distances can then be used to pack the extracted bits of each integer to O (n) bits. Perfect word hash function constructed with our method using these shift distances allows a batch of mn integers with m integers packed in a word to be hashed in O (n) time. (C) 2017 Elsevier B.V. All rights reserved.
The Set Covering problem is an NP-complete problem. A recent result of Lund and Yanakakis establishes that Set Covering cannot be approximated with ratio c log(2) n for any c<1/4 unless all NP problems are solvable...
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The Set Covering problem is an NP-complete problem. A recent result of Lund and Yanakakis establishes that Set Covering cannot be approximated with ratio c log(2) n for any c<1/4 unless all NP problems are solvable in DTIME(n(polylog n)). Th, known greedy algorithm for Set Covering delivers a ratio of H(d)=Sigma(i=1)(d)1/i, where d is the size of the largest set, a value bounded by 1 + log d. Here we describe an improved version of the greedy algorithm and show that its worst case ratio bound is, H(d)-1/6.
The inference problem in propositional logic realizes a strong connection between Artificial Intelligence and Operational Research. It is now well-known that this problem can be formulated as a constraint satisfaction...
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The inference problem in propositional logic realizes a strong connection between Artificial Intelligence and Operational Research. It is now well-known that this problem can be formulated as a constraint satisfaction problem (CSP), whose system has a generalized covering type (we recall that a CSP consists in proving the emptiness of a domain defined by a set of diophantine constraints, or the existence of a solution). We propose a new method - denoted by FAST (Fast Algorithm for the constraint Satisfaction Test problems) - which allows an efficient solution of the CSP instances for logical inference. Computational results are reported for 3-SAT, 4-SAT and system expert type instances.
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