1,239,697 research outputs found
Finding the maximum and minimum
AbstractWe consider the problem of finding the maximum out of a list of n ordered items with binary comparisons where the pth fraction of the answers may be false. It is shown that the maximum can be determined iff p < 12 and that a successful strategy needs Î(11âp)n questions. A few similar problems are also discussed, including the problem of finding the maximum and minimum simultaneously with lies and in the nuts and bolts model
Pareto optimality in house allocation problems
We study Pareto optimal matchings in the context of house allocation problems. We present an O(\sqrt{n}m) algorithm, based on Gales Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching
Optimal General Matchings
Given a graph and for each vertex a subset of the
set , where denotes the degree of vertex
in the graph , a -factor of is any set such that
for each vertex , where denotes the number of
edges of incident to . The general factor problem asks the existence of
a -factor in a given graph. A set is said to have a {\em gap of
length} if there exists a natural number such that and . Without any restrictions the
general factor problem is NP-complete. However, if no set contains a gap
of length greater than , then the problem can be solved in polynomial time
and Cornuejols \cite{Cor} presented an algorithm for finding a -factor, if
it exists. In this paper we consider a weighted version of the general factor
problem, in which each edge has a nonnegative weight and we are interested in
finding a -factor of maximum (or minimum) weight. In particular, this
version comprises the minimum/maximum cardinality variant of the general factor
problem, where we want to find a -factor having a minimum/maximum number of
edges.
We present an algorithm for the maximum/minimum weight -factor for the
case when no set contains a gap of length greater than . This also
yields the first polynomial time algorithm for the maximum/minimum cardinality
-factor for this case
Tight Bounds on the Synthesis of 3-bit Reversible Circuits: NFT Library
The reversible circuit synthesis problem can be reduced to permutation group.
This allows Schreier-Sims Algorithm for the strong generating set-finding
problem to be used to find tight bounds on the synthesis of 3-bit reversible
circuits using the NFT library. The tight bounds include the maximum and
minimum length of 3-bit reversible circuits, the maximum and minimum cost of
3-bit reversible circuits. The analysis shows better results than that found in
the literature for the lower bound of the cost. The analysis also shows that
there are 1960 universal reversible sub-libraries from the main NFT library.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1101.438
Results on Binary Linear Codes With Minimum Distance 8 and 10
All codes with minimum distance 8 and codimension up to 14 and all codes with
minimum distance 10 and codimension up to 18 are classified. Nonexistence of
codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new
exact bounds for binary linear codes. Primarily two algorithms considering the
dual codes are used, namely extension of dual codes with a proper coordinate,
and a fast algorithm for finding a maximum clique in a graph, which is modified
to find a maximum set of vectors with the right dependency structure.Comment: Submitted to the IEEE Transactions on Information Theory, May 2010 To
be presented at the ACCT 201
Two-channel linear phase FIR QMF bank minimax design via global nonconvex optimization programming
In this correspondence, a two-channel linear phase finite impulse response (FIR) quadrature mirror filter (QMF) bank minimax design problem is formulated as a nonconvex optimization problem so that a weighted sum of the maximum amplitude distortion of the filter bank, the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter is minimized subject to specifications on these performances. A modified filled function method is proposed for finding the global minimum of the nonconvex optimization problem. Computer numerical simulations show that our proposed design method is efficient and effective
Profile-Based Optimal Matchings in the Student-Project Allocation Problem
In the Student/Project Allocation problem (spa) we seek to assign students to individual or group projects offered by lecturers. Students provide a list of projects they find acceptable in order of preference. Each student can be assigned to at most one project and there are constraints on the maximum number of students that can be assigned to each project and lecturer. We seek matchings of students to projects that are optimal with respect to profile, which is a vector whose rth component indicates how many students have their rth-choice project. We present an efficient algorithm for finding agreedy maximum matching in the spa context â this is a maximum matching whose profile is lexicographically maximum. We then show how to adapt this algorithm to find a generous maximum matching â this is a matching whose reverse profile is lexicographically minimum. Our algorithms involve finding optimal flows in networks. We demonstrate how this approach can allow for additional constraints, such as lecturer lower quotas, to be handled flexibly
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