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Recall the KNAPSACK problem (Section 64): we are given integer weights w 1 , , wn and integer values v1 , , vn for n items We are also given a weight capacity W and a goal g (the former is present in the original optimization problem, the latter is added to make it a search problem) We seek a set of items whose total weight is at most W and whose total value is at least g As always, if no such set exists, we should say so In Section 64, we developed a dynamic programming scheme for KNAPSACK with running time O(nW ), which we noted is exponential in the input size, since it involves W rather than log W And we have the usual exhaustive algorithm as well, which looks at all subsets of items all 2n of them Is there a polynomial algorithm for KNAPSACK Nobody knows of one But suppose that we are interested in the variant of the knapsack problem in which the integers are coded in unary for instance, by writing IIIIIIIIIIII for 12 This is admittedly an exponentially wasteful way to represent integers, but it does de ne a legitimate problem, which we could call UNARY KNAPSACK It follows from our discussion that this somewhat arti cial problem does have a polynomial algorithm A different variation: suppose now that each item s value is equal to its weight (all given in binary), and to top it off, the goal g is the same as the capacity W (To adapt the silly break-in story whereby we rst introduced the knapsack problem, the items are all gold nuggets, and the burglar wants to ll his knapsack to the hilt) This special case is tantamount to nding a subset of a given set of integers that adds up to exactly W Since it is a special case of KNAPSACK, it cannot be any harder But could it be polynomial As it turns out, this problem, called SUBSET SUM, is also very hard At this point one could ask: If SUBSET SUM is a special case that happens to be as hard as the general KNAPSACK problem, why are we interested in it The reason is simplicity In the complicated calculus of reductions between search problems that we shall develop in this chapter, conceptually simple problems like SUBSET SUM and 3 SAT are invaluable 238.

With few exceptions, such as testing pupillary reactions and examination of the skin for abnormalities of color and sweating, the neurologist tends to be casual in evaluating the function of the autonomic nervous system Nonetheless, several simple but informative tests can be used to con rm one s clinical impressions and to elicit abnormalities of autonomic function that may aid in diagnosis A combination of tests is usually necessary, because certain ones are particularly sensitive to abnormalities of sympathetic function and others to parasympathetic or baroreceptor afferent function These are described below and are summarized in Table 26-1 A scheme for the examination of pupillary abnormalities has been presented in Fig 14-8 Responses of Blood Pressure and Heart Rate to Changes in Posture and Breathing These are among the simplest and most important tests of autonomic function and are currently automated in most laboratories McLeod and Tuck state that in changing from the recumbent to the standing position, a fall of more than 30 mmHg systolic and 15 mmHg diastolic is abnormal; others give gures of 20 and 10 mmHg They caution that the arm on which the cuff is placed must be held horizontally when standing, so that the decline in arm pressure will not be obscured by the added hydrostatic pressure The main cause of an orthostatic drop in blood pressure is hypovolemia In the context of recurrent fainting, however, an excessive drop re ects inadequate sympathetic vasoconstrictor activity The use of a tilt table, as described on page 330, is the most sensitive means of inducing orthostatic changes and also elicits

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