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NP-Completeness
(a) Suppose you are given an algorithm A to solve the CLIQUE decision problem. That is, A(G, k) will decide whether graph G has a clique of size k. Give an algorithm to find the vertices of a k-clique in a graph G using only calls to A, if any such k-clique exists.
(b) Suppose you are given an algorithm B to solve the LARGEST-COMMON-SUBGRAPH decision problem. Give an algorithm to find a subgraph of size k that appears in both graphs G1 and G2, using only calls to B, if any such subgraph exists.
A two-stage trickling filter plant treats 291.7 m3/h of municipal wastewater that has a BOD5 of 200 mg/L. The two filters have equal dimensions (depth = 1.68 m; diameter = 21.3 m), and each has a recycle ratio of 1.0
A concrete mix with a 3-inch slump, w/c ratio of 0.50, and sand with a fineness modulus of 2.4 contains 1700 lb/yd^3 of coarse aggregate. Compute the required weight of coarse aggregate per cubic yard.
Select the best rectangular HSS for a column to support a service dead load of 30 kips and a service live load of 90 kips. The member is 22 feet long and is pinned at the ends.
Given a type of material used in a wire with diameter (d = 0.25 in) that stretches 2.3 inches while 80 feet of length is under tensile load of 1800 pounds. Find the elastic modulus of the material used to construct the wire.
A cutting 9 m deep is to be excavated in saturated clay of unit weight 19 kN/m3. The design shear strength parameters are cu = 30 kN/ m2 and fu = 0. A hard stratum underlies the clay at a depth of 11 m below ground level.
Aluminum cans in the 1970's were considerably heavier than they arenow. For a 0.355-L (12 oz) aluminum can, with mass 0.0205 kg, andusing a 25 percent recycling rate, find the primary energy requiredto produce the aluminum in one such can.
A multiple-piston hydraulic jack has two output pistons, each with an area of 250 cm^2. The input piston, whose area is 25 cm^2, is concerned to a lever that has a mechanical advantage of 9:1.
A 30mm pipe X 460mm rectangular duct carries air. What size square conduit is needed to transport 4m cube per sec of water at a distance of 45m and head loss of of 1.08m.
The tank has an inner diameter of 1.5 m and a wall thickness of 18 mm. If the pressure in the tank is p=1.20MPa, determine the force in the 16 bolts that are used to attach the cap to the tank. Also, specify the state of stress in the wall of the ..
The inflow to a small reservoir during a storm may be described by the equations Q=1000(1-e^-kt) where Q= flow in cfs k= runoff rate = 1.0 per hour t = time in hours The outflow through the dam gates is held constant at 800 cfs.
A 10 m long built-up beam is to be fabricated from a universal section beam (UB) and two 'C' channel sections (as indicated). The beams are joined by bolts, with the allowable shear load in each bolt being 12 kN.
Calculate the max capillary rise of water between 2 verticle glass plates spaced .25mm apart and the minimum capillary drop if the same plates are placed .25mm apart are in mercury
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