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Algorithms for Transposition Invariant String Matching (Extended Abstract)
 Journal of Algorithms
, 2002
"... Given strings A and B over an alphabet Σ ⊆ U, where U is some numerical universe closed... ..."
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Cited by 9 (5 self)
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Given strings A and B over an alphabet Σ ⊆ U, where U is some numerical universe closed...
TWOWAY CHAINING WITH REASSIGNMENT
"... Abstract. We present an algorithm for hashing ⌊ αn ⌋ elements into a table with n separate chains that requires O(1) deterministic worstcase insert time, and O(1) expected worstcase search time for constant α. We exploit the connection between twoway chaining and random graph theory in our techni ..."
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Cited by 3 (1 self)
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Abstract. We present an algorithm for hashing ⌊ αn ⌋ elements into a table with n separate chains that requires O(1) deterministic worstcase insert time, and O(1) expected worstcase search time for constant α. We exploit the connection between twoway chaining and random graph theory in our techniques.
Improved Multiunit Auction Clearing Algorithms with Interval (MultipleChoice) Knapsack Problems
"... Abstract. We study the interval knapsack problem (IKP), and the interval multiplechoice knapsack problem (IMCKP), as generalizations of the classic 0/1 knapsack problem (KP) and the multiplechoice knapsack problem (MCKP), respectively. Compared to singleton items in KP and MCKP, each item i in I ..."
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Cited by 1 (0 self)
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Abstract. We study the interval knapsack problem (IKP), and the interval multiplechoice knapsack problem (IMCKP), as generalizations of the classic 0/1 knapsack problem (KP) and the multiplechoice knapsack problem (MCKP), respectively. Compared to singleton items in KP and MCKP, each item i in IKP and IMCKP is represented by a ([ai, bi], pi) pair, where integer interval [ai, bi] specifies the possible range of units, and pi is the unitprice. Our main results are a FPTAS for IKP with time O(nlog n + n/ǫ 2) and a FPTAS for IMCKP with time O(nm/ǫ), and pseudopolynomialtime algorithms for both IKP and IMCKP with time O(nM) and space O(n + M). Here n, m, and M denote number of items, number of item sets, and knapsack capacity respectively. We also present a 2approximation of IKP and a 3approximation of IMCKP both in linear time. We apply IKP and IMCKP to the singlegood multiunit sealedbid auction clearing problem where M identical units of a single good are auctioned. We focus on two bidding models, among them the interval model allows each bid to specify an interval range of units, and XORinterval model allows a bidder to specify a set of mutually exclusive interval bids. The interval and XORinterval bidding models correspond to IKP and IMCKP respectively, thus are solved accordingly. We also show how to compute VCG payments to all the bidders with an overhead of O(log n) factor. Our results for XORinterval bidding model imply improved algorithms for the piecewise constant bidding model studied by Kothari et al. [18], improving their algorithms by a factor of Ω(n). 1