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Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 822 (39 self)
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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
On graph kernels: Hardness results and efficient alternatives
 IN: CONFERENCE ON LEARNING THEORY
, 2003
"... As most ‘realworld’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances tha ..."
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Cited by 185 (5 self)
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that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered. This paper investigates kernels on labeled directed graphs with general structure. It is shown that computing a strictly positive definite graph kernel is at least as hard as solving the graph isomorphism
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Hardness results for homology localization
 In SODA ’10: Proc. 21st Ann. ACMSIAM Sympos. Discrete Algorithms (2010
"... We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1norm of a cycle. Two main results are presented. First, we prove the problem is NPhard to approximate w ..."
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Cited by 17 (1 self)
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We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1norm of a cycle. Two main results are presented. First, we prove the problem is NPhard to approximate
Hardness results for approximating the bandwidth
, 2009
"... The bandwidth of an nvertex graph G is the minimum value b such that the vertices of G can be mapped to distinct integer points on a line without any edge being stretched to a distance more than b. Previous to the work reported here, it was known that it is NPhard to approximate the bandwidth with ..."
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Cited by 5 (0 self)
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within a factor better than 3/2. We improve over this result in several respects. For certain classes of graphs (such as cycles of cliques) for which it is easy to approximate the bandwidth within a factor of 2, we show that approximating the bandwidth within a ratio better than 2 is NPhard
Hardness Results for Cake Cutting
, 2003
"... Fair cakecutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to "cut" pieces of the cake ..."
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Cited by 6 (0 self)
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Fair cakecutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to "cut" pieces of the cake into specified ratios. Many
Hardness Results for Tournament Isomorphism and
, 2007
"... A tournament is a graph in which each pair of distinct vertices is connected by exactly one directed edge. Tournaments are an important graph class, for which isomorphism testing seems to be easier to compute than for the isomorphism problem of general graphs. We show that tournament isomorphism and ..."
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Cited by 1 (1 self)
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and tournament automorphism is hard under DLOGTIME uniform AC 0 manyone reductions for the complexity classes NL, C=L, PL (probabilistic logarithmic space), for logarithmic space modular counting classes ModkL with odd k ≥ 3 and for DET, the class of problems, NC 1 reducible to the determinant. These lower
Optimal Hardness Results for Maximizing . . .
"... We consider the problem of finding a monomial (or a term) that maximizes the agreement rate with a given set of examples over the Boolean hypercube. The problem is motivated by learning of monomials in the agnostic framework of Haussler [12] and Kearns et al. [17]. Finding a monomial with the highes ..."
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with the highest agreement rate was proved to be NPhard by Kearns and Li [15]. BenDavid et al. gave the first inapproximability result for this problem, proving that the maximum agreement rate is NPhard to approximate within 770 767 − ɛ, for any constant ɛ> 0 [5]. The strongest known hardness
Hardness Result for TSP with Neighborhoods
, 2000
"... . In TSP with neighborhoods (TSPN) we are given a collection X of k polygonal regions, called neighborhoods, with totally n vertices, and we seek the shortest tour that visits each neighborhood. The Euclidean TSP is a special case of the TSPN problem, so TSPN is also NPhard. In this paper we s ..."
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. In TSP with neighborhoods (TSPN) we are given a collection X of k polygonal regions, called neighborhoods, with totally n vertices, and we seek the shortest tour that visits each neighborhood. The Euclidean TSP is a special case of the TSPN problem, so TSPN is also NPhard. In this paper we
Results 1  10
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1,839,744