Beyond p and np by pasin manurangsi a dissertation submitted in partial satisfaction of the requirements for the degree of doctor of philosophy in computer science in the graduate division of the university of california, berkeley committee in charge. Its not as easy as people say, especially with small hands. In computational complexity theory, a problem is npcomplete when it can be solved by a. Nphard problems there is an easy proof that maxclique is nphard, using a reduction from maxindset. Alll2np canbereducedtosat i 9polynomialg suchthatx 2l gx 2sat i. Nphardness many problems in ai are nphard or worse what does this mean. These are some of the hardest problems in cs identifying a problem as np hard means. Our np hardness reductions are quasilinearsize and thus show nearly full exponential time is required, assuming the eth. Nphardness of computing circuit complexity drops schloss.
Nphardness a language l is called nphard iff for every l. Mcsp is not known to be nphard, yet an efficient algorithm for this problem also seems very unlikely. We prove the np hardness using a reduction of the np complete problem from cs 570 at university of southern california. We show that some basic linear control design problems are nphard, implying that. Professor luca trevisan, cochair professor prasad raghavendra, cochair.
Nphard and npcomplete problems 7 if this decision problem cannot be solved by an algorithm of complexity pn for some polynomial p, then it cannot be solved by an algorithm of complexity pjvj 01 knapsack input size qqn for knapsack decision problem is q x. The usual nphardness proof uses turing machines, a simple theoretical computer designed in 1936. Department of computer science, carnegie mellon university. Unweighted coalitional manipulation under the borda rule is nphard. In their recent overview on ais war on manipulation fal iszewski and procaccia 2010 write. The maximum clique size problem, or simply maxclique, is to compute, given a graph, the number of nodes in its largest complete subgraph. You probably shouldnt waste time trying to find a polynomial time solution if you find a polynomial time solution, either you have a bug. Nphardness problems for target controllability of complex.
Supported by nsf grants ccf0747250 and ccf0915893, and by a sloan fellowship. Nphardness of some linear control design problems mit. Our results signi cantly extend gv05, which only show nphardness for d 1. Your job is to write a program that determines a route from the depot via all locations. We prove the np hardness using a reduction of the np. Its my progress after one month of practicing this piece, so it isnt perfect yet. A language in l is called npcomplete iff l is nphard and l.
On the nphardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback. A recent proof of nphardness of euclidean sumofsquares clustering, due to drineas et al. Suppose that we wanted to write those numbers in unary. Nphardness of some euclidean problems of partitioning a finite set of points article pdf available in computational mathematics and mathematical physics 585 may 2018 with 72 reads.
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