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We present a preprocessing algorithm to make certain polynomial algorithms strongly polynomial. The running time of some of the known combinatorial optimization algorithms depends on the size of the objective function w. Our preprocessing algorithm replaces w by an integral valued w whose size is polynomially bounded in the size of the combinatorial structure and which yields the same set of optimal...
We assume a parallel RAM model which allows both concurrent writes and concurrent reads of global memory. Our algorithms are randomized: each processor is allowed an independent random number generator. However our stated resource bounds hold for worst case input with overwhelming likelihood as the input size grows. We give a new parallel algorithm for integer sorting where the integer keys are restricted...
The purpose of this paper is to resolve several open problems in the current literature on Boolean circuits, communication complexity, and hashing functions. These lower bound results share the common feature that their proofs utilize probabilistic arguments in an essential way. Specifically, we prove that, to compute the majority function of n Boolean variables, the size of any depth-3 monotone circuit...
Decision procedures are provided for checking the satisfiability of a formula in each of the three systems TCg. TCb and TCf defined in [LS]. The procedures for TCg and TCf run in non-deterministic time 22on where n is the size of the formula and c is a constant. The procedure for TCb runs in non-deterministic time 22on2. A deterministic exponential lower bound is proved for the three systems. All...
We define a p-party ping-pong protocol and its security problem, along the lines of Dolev and Yao's definition for twoparty ping-pong protocol. In the case of two parties, it was assumed, with no loss of generality, that there exists a single saboteur in the net and the protocol was defined to be secure iff it was secure against the active interventions of one saboteur. We show that for more than...
We consider the problem of computing a set of algebraic functions that involve extracting roots of various degrees. We show that the complexity of computing a large class of algebraic functions is determined by the Galois group G of the extension generated by the functions. We relate the minimum cost to decomposing G into a sequence of normal subgroups such that each factor group is cyclic. We derive...
We examine the class of matrices that satisfy Commoner's sufficient condition for total unimodularity [C], which we call restricted totally unimodular (RTUM). We show that a matrix is RTUM if and only if it can be decomposed in a very simple way into the incidence matrices (or their transposes) of bipartite graphs or directed graphs, and give a linear time algorithm to perform this task. Based on...
We consider uniform circuit complexity, introduced by Borodin as a model of parallel complexity. Three main results are presented. First, we show that simultaneous size/depth of uniform circuits is the same as space/time of alternating Turing machines, with depth and time within a constant factor and likewise log(size) and space. Second, we apply this to characterize the class of polynomial size and...
Fully polynomial approximation algorithms for knapsack problems are presented. These algorithms are based on ideas of Ibarra and Kim, with modifications which yield better time and space bounds, and also tend to improve the practicality of the procedures. Among the principal improvements are the introduction of a more efficient method of scaling and the use of a median-finding routine to eliminate...
A combinatorial problem related to storage allocation is analyzed. The problem falls into a class of NP-complete, one-dimensional bin-packing problems. We propose an iterative approximation algorithm and show that it is superior to an earlier heuristic presented for this problem. The bulk of the paper is devoted to the proof of a worst-case performance bound.
A proposed method for testing printed circuit boards for the existence of possible (undesired) short circuits transforms the test minimization problem into one of finding minimum vertex colorings of certain special graphs, called line-of-sight graphs. Under certain assumptions on the possible types of short circuits, we analyze the structure of such graphs and show that a well-known and efficient...
There are several situations that we are trying more or less to model. One arises from the standard IQ test in which a person is given a finite sequence of integers and asked to produce the next integer in the sequence. Another is provided by the following grossly simplified view of one aspect of physics: Consider a physicist who is trying to find a law to explain a growing body of experimental data...
We investigate the size of sets of computable functions using category-theoretic methods (in the sense of the Baire Category theorem). Constructive definitions of no-where dense and meagre set are given and applied to several problems. In particular we apply it to subrecursive degree structures and to a comparison of the power of deterministic and nondeterministic time bounded oracle machines.
In this paper we consider polynomial-time algorithms for bin packing and their applications. The previously studied FIRST FIT and BEST FIT algorithms are shown to be special cases of a more generalized class of algorithms which all have similar worst case behavior. Linear time algorithms are then introduced which, though "faster" than FIRST FIT and BEST FIT, have the same, or better, worst...
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