41,213 research outputs found
To Not Understand, but Not Misunderstand: Wittgenstein on Shakespeare
Wittgenstein's lack of sympathy for Shakespeare's works has been well noted by George Steiner and Harold Bloom among others. Wittgenstein writes in 1950, for instance: "It seems to me as though his pieces are, as it were, enormous sketches, not paintings; as though they were dashed off by someone who could permit himself anything, so to speak. And I understand how someone may admire this & call it supreme art, but I don't like it." Of course, the animosity of one great mind for another has its own interest. But the interest here is increased by two factors: (1) Wittgenstein's brief but specific critique of Shakespeare's similes, of interest particularly since he identifies his own philosophical strength half-deprecatingly but still seriously as one of crafting beautiful similes; and (2) Wittgenstein's and Shakespeare's shared concern, as revealed in Stanley Cavell's writings, with the human impulse to skepticism. The present paper considers the importance of these two factors in weighing Wittgenstein's judgment. It suggests that Wittgenstein's frequent charge that Shakespeare is "completely unrealistic" is not a misunderstanding of the Bard (Wittgenstein distinguishes his "failure to understand" from others' willingness to misunderstand Shakespeare) but rather an expression of Wittgenstein's anxiety over Shakespeare's wholly original use of language to represent the sound of the raw motives to skepticism
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
Perfect Omniscience, Perfect Secrecy and Steiner Tree Packing
We consider perfect secret key generation for a ``pairwise independent
network'' model in which every pair of terminals share a random binary string,
with the strings shared by distinct terminal pairs being mutually independent.
The terminals are then allowed to communicate interactively over a public
noiseless channel of unlimited capacity. All the terminals as well as an
eavesdropper observe this communication. The objective is to generate a perfect
secret key shared by a given set of terminals at the largest rate possible, and
concealed from the eavesdropper.
First, we show how the notion of perfect omniscience plays a central role in
characterizing perfect secret key capacity. Second, a multigraph representation
of the underlying secrecy model leads us to an efficient algorithm for perfect
secret key generation based on maximal Steiner tree packing. This algorithm
attains capacity when all the terminals seek to share a key, and, in general,
attains at least half the capacity. Third, when a single ``helper'' terminal
assists the remaining ``user'' terminals in generating a perfect secret key, we
give necessary and sufficient conditions for the optimality of the algorithm;
also, a ``weak'' helper is shown to be sufficient for optimality.Comment: accepted to the IEEE Transactions on Information Theor
Optimal Flood Control
A mathematical model for optimal control of the water levels in a chain of
reservoirs is studied. Some remarks regarding sensitivity with respect to the time horizon, terminal cost and forecast of inflow are made
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