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Algorithms and Complexity Concerning the Preemptive Scheduling of Periodic, RealTime Tasks on One Processor
 RealTime Systems
, 1990
"... We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the pape ..."
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Cited by 179 (13 self)
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We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the paper, that all parameters are indeed integers. We then give as our main lemma both necessary and sufficient conditions for a task system to be feasible on one processor. Although these conditions cannot, in general, be tested efficiently (unless P = NP), they do allow us to give efficient algorithms for deciding feasibility on one processor for certain types of periodic task systems. For example, we give a pseudopolynomial time algorithm for synchronous systems whose densities are bounded by a fixed constant less than 1. This algorithm represents an exponential improvement over the previous best algorithm. We also give a polynomialtime algorithm for systems having a fixed number of distinct typ...
Tight Bounds and 2Approximation Algorithms for Integer Programs with Two Variables per Inequality
 Mathematical Programming
, 1992
"... . The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NPcomplete, even when all variables are binary. This paper deals with integer linear minimization problems in n variables subject to m linear constraints with at most tw ..."
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Cited by 41 (5 self)
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. The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NPcomplete, even when all variables are binary. This paper deals with integer linear minimization problems in n variables subject to m linear constraints with at most two variables per inequality, and with all variables bounded between 0 and U . For such systems, a 2\Gammaapproximation algorithm is presented that runs in time O(mnU 2 log(Un 2 =m)), so it is polynomial in the input size if the upper bound U is polynomially bounded. The algorithm works by finding first a superoptimal feasible solution that consists of integer multiples of 1 2 . That solution gives a tight bound on the value of the minimum. It further more has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem. These properties are a generalization of the properties of the vertex cover problem. The algorithm described is, ...
Pseudorandom number generation within cryptographic algorithms: the dss case
 in Proceedings of advances in cryptology’97, Lecture Notes in Computer Science
, 1997
"... The DSS signature algorithm requires the signer to generate a new random number with every signature. We show that if random numbers for DSS are generated using a linear congruential pseudorandom number generator (LCG) then the secret key can be quickly recovered after seeing a few signatures. This ..."
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Cited by 24 (1 self)
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The DSS signature algorithm requires the signer to generate a new random number with every signature. We show that if random numbers for DSS are generated using a linear congruential pseudorandom number generator (LCG) then the secret key can be quickly recovered after seeing a few signatures. This illustrates the high vulnerability of the DSS to weaknesses in the underlying random number generation process. It also con rms, that a sequence produced by LCG is not only predictable as has been known before, but should be used with extreme caution even within cryptographic applications that would appear to protect this sequence. The attack we present applies to truncated linear congruential generators as well, and can be extended to any pseudo random generator that can be described via modular linear equations.
Fast 2Variable Integer Programming
 Integer Programming and Combinatorial Optimization, IPCO 2001, volume 2081 of LNCS
, 2001
"... We show that a 2variable integer program defined by m constraints involving coefficients with at most s bits can be solved with O(m+s log m) arithmetic operations or with O(m+logm log s)M(s) bit operations, where M(s) is the time needed for sbit integer multiplication. ..."
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Cited by 7 (3 self)
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We show that a 2variable integer program defined by m constraints involving coefficients with at most s bits can be solved with O(m+s log m) arithmetic operations or with O(m+logm log s)M(s) bit operations, where M(s) is the time needed for sbit integer multiplication.
Fast Reduction of Ternary Quadratic Forms
"... We show that a positive definite integral ternary form can be reduced with O(M(s)log s) bit operations, where s is the binary encoding length of the form and M(s) is the bitcomplexity of sbit integer multiplication. ..."
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Cited by 5 (0 self)
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We show that a positive definite integral ternary form can be reduced with O(M(s)log s) bit operations, where s is the binary encoding length of the form and M(s) is the bitcomplexity of sbit integer multiplication.
A Decade of Combinatorial Optimization
, 1997
"... This paper offers a brief overview of the developments in combinatorial optimization during the past decade. We discuss improvements in polynomialtime algorithms for problems on graphs and networks, and review the methodological and computational progress in linear and integer optimization. Some of ..."
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Cited by 4 (0 self)
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This paper offers a brief overview of the developments in combinatorial optimization during the past decade. We discuss improvements in polynomialtime algorithms for problems on graphs and networks, and review the methodological and computational progress in linear and integer optimization. Some of the more prominent software packages in these areas are mentioned. With respect to obtaining approximate solutions to NPhard problems, we survey recent positive and negative results on polynomialtime approximability and summarize the advances in local search.