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15
A Fast and Simple Algorithm for the Money Changing Problem
 ALGORITHMICA
, 2007
"... The Money Changing Problem (MCP) can be stated as follows: Given k positive integers a1 < ···< ak and a query integer M, is there a linear combination ∑ i ci ai = M with nonnegative integers ci,a decomposition of M? If so, produce one or all such decompositions. The largest integer without such a ..."
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Cited by 10 (5 self)
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The Money Changing Problem (MCP) can be stated as follows: Given k positive integers a1 < ···< ak and a query integer M, is there a linear combination ∑ i ci ai = M with nonnegative integers ci,a decomposition of M? If so, produce one or all such decompositions. The largest integer without such a decomposition is called the Frobenius number g(a1,...,ak). A data structure called the residue table of a1 words can be used to compute the Frobenius number in time O(a1). We present an intriguingly simple algorithm for computing the residue table which runs in time O(ka1), with no additional memory requirements, outperforming the best previously known algorithm. Simulations show that it performs well even on “hard ” instances from the literature. In addition, we can employ the residue table to answer MCP decision instances in constant time, and a slight modification of size O(a1) to compute one decomposition for a query M. Note that since both computing the Frobenius number and MCP (decision) are NPhard, one cannot expect to find an algorithm that is polynomial in the size of the input, i.e., in k, log ak, and log M. We then give an algorithm which, using a modification of the residue table, also constructible in O(ka1) time, computes all decompositions of a query integer M. Its worstcase running time is O(ka1) for each
Combinatorics of Geometrically Distributed Random Variables: Value and Position of the rth LefttoRight Maximum
 Discrete Math
"... For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1. ..."
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Cited by 8 (5 self)
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For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1.
Analyzing the Stochastic Complexity via Tree Polynomials
, 2005
"... Stochastic complexity of a data set is defined as the shortest possible code length for the data obtainable by using some fixed set of models. This measure ..."
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Cited by 6 (5 self)
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Stochastic complexity of a data set is defined as the shortest possible code length for the data obtainable by using some fixed set of models. This measure
Decontamination of hypercubes by mobile agents
 Networks
"... In this paper we consider the decontamination problem in a hypercube network of size n. The nodes of the network are assumed to be contaminated and they have to be decontaminated by a sufficient number of agents. An agent is a mobile entity that asynchronously moves along the network links and decon ..."
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Cited by 5 (1 self)
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In this paper we consider the decontamination problem in a hypercube network of size n. The nodes of the network are assumed to be contaminated and they have to be decontaminated by a sufficient number of agents. An agent is a mobile entity that asynchronously moves along the network links and decontaminates all the nodes it touches. A decontaminated node that is not occupied by an agent is recontaminated if it has a contaminated neighbour. We consider some variations of the model based on the capabilities of mobile agents: locality, where the agents can only access local information; visibility, where they can “see ” the state of their neighbours; and cloning, where they can create copies of themselves. We also consider synchronicity as an alternative system requirement. For each model, we design a decontamination strategy and we make several observations. For agents with locality, our strategy is based on the use of a coordinator that leads the other agents. Our strategy results in an optimal number of agents, Θ( √ n), and requires O(n log n) moves and O(n log n) time log n steps. For agents with visibility, we assume that the agents can move autonomously. In this setting, our decontamination strategy achieves an optimal time complexity (logn time steps), but the number of agents increases to n 2. Finally, we show that when the agents have the capability to clone combined with either visibility or synchronicity, we can reduce the move complexity—which becomes optimal—at the expense of an increase in the number of agents.
Coinductive Counting With Weighted Automata
, 2002
"... A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; ..."
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Cited by 4 (0 self)
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A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute an expression (in terms of stream constants and operators) that represents the stream of all counts.
On the spectrum of the ZhangZagier height
 Biological Cybernetics
, 1997
"... Abstract. From recent work of Zhang and of Zagier, we know that their height H(α) is bounded away from 1 for every algebraic number α different from 0, 1, 1/2 ± √ −3/2. The study of the related spectrum is especially interesting, for it is linked to Lehmer’s problem and to a conjecture of Bogomolov ..."
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Cited by 3 (1 self)
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Abstract. From recent work of Zhang and of Zagier, we know that their height H(α) is bounded away from 1 for every algebraic number α different from 0, 1, 1/2 ± √ −3/2. The study of the related spectrum is especially interesting, for it is linked to Lehmer’s problem and to a conjecture of Bogomolov. After recalling some definitions, we show an improvement of the socalled ZhangZagier inequality. To achieve this, we need some algebraic numbers of small height. So, in the third section, we describe an algorithm able to find them, and we give an algebraic number with height 1.2875274... discovered in this way. This search up to degree 64 suggests that the spectrum of H(α) mayhave a limit point less than 1.292. We prove this fact in the fourth part. 1.
Coinductive counting: bisimulation in enumerative combinatorics (extended abstract). Report SENR0129, CWI, 2001. Available at URL http://www.cwi.nl. Also in
 L. Moss (Ed.), The Proc. CMCS’02, ENTCS, Vol. 65, Elsevier Science B.V
, 2002
"... Coinductive counting: bisimulation in enumerative combinatorics (extended abstract) ..."
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Coinductive counting: bisimulation in enumerative combinatorics (extended abstract)
Asymptotic Estimates for Generalized Stirling Numbers ABSTRACT
, 1999
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Elements of stream calculus
 In MFPS 2001, ENTCS 45
, 2001
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.