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Testing Orientability for Matroids is NPcomplete
 Advances in Applied Mathematics (special issure: \in the honour of
, 1999
"... Matroids and oriented matroids are fundamental objects in combinatorial geometry. While matroids model the behavior of... ..."
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Matroids and oriented matroids are fundamental objects in combinatorial geometry. While matroids model the behavior of...
OneinTwoMatching Problem is NPcomplete
, 2006
"... Abstract. 2dimensional Matching Problem, which requires to find a matching of left to rightvertices in a balanced 2nvertex bipartite graph, is a wellknown polynomial problem, while various variants, like the 3dimensional analogoue (3DM, with triangles on a tripartite graph), or the Hamiltonian ..."
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and Travelling Salesman Problem being NPcomplete. In this paper we show that a small modification of the 2dimensional Matching and Assignment Problems in which for each i ≤ n/2 it is required that either π(2i − 1) = 2i − 1 or π(2i) = 2i, is a NPcomplete problem. The proof is by linear reduction from SAT (or
A Brief History of NPCompleteness, 1954–2012
 DOCUMENTA MATH.
, 2012
"... The year 2012 marks the 40th anniversary of the publication of the influential paper “Reducibility among combinatorial problems ” by Richard Karp [37]. This paper was the first to demonstrate the wide applicability of the concept now known as NPcompleteness, which had been introduced the previous y ..."
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The year 2012 marks the 40th anniversary of the publication of the influential paper “Reducibility among combinatorial problems ” by Richard Karp [37]. This paper was the first to demonstrate the wide applicability of the concept now known as NPcompleteness, which had been introduced the previous
Inapproximability of NPComplete Variants of Nash Equilibrium
, 20113
"... In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an εapproximate Nash equilibrium with nearoptimal value in a twoplayer game is as hard as finding a hidden clique of size O(logn) in the random graph G(n,1/2). This raises the question of whether a similar intractab ..."
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Clique problem. This is in contrast to the basic problem (finding a Nash equilibrium with no optimization criteria) where more sophisticated algorithms, achieving better approximations, are known. Unlike basic Nash equilibrium, which is in PPAD, optimal (maximum value) Nash equilibrium is NPhard. We
Numerical Evidence for Phase Transitions of NPComplete Problems for Instances Drawn from
, 2011
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Reconstructing Polyatomic Structures from Discrete XRays: NPCompleteness Proof for Three Atoms
 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science, LNCS vol 1450
, 1998
"... We address a discrete tomography problem that arises in the study of the atomic structure of crystal lattices. A polyatomic structure T can be defined as an integer lattice in dimension D ≥ 2, whose points may be occupied by c distinct types of atoms. To “analyze ” T, we conduct ℓ measurements that ..."
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Cited by 11 (4 self)
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. As shown in another article by the same authors, [4], this problem is also NPcomplete for c ≥ 6 atoms, even for dimension D = 2 and axisparallel Xrays. The authors of [4] conjecture that the problem remains NPcomplete for c = 3, 4, 5, although, as they point out, the proof idea in [4] does not seem
Manhattan Channel Routing is NPComplete under Truly Restricted Settings
, 1996
"... Settling an open problem that is over ten years old, we show that Manhattan channel routing  with doglegs allowed  is NPcomplete when all nets have two terminals. This result fills the gap left by Szymanski [Szy85], who showed the NPcompleteness for nets with four terminals. Answering a question ..."
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Settling an open problem that is over ten years old, we show that Manhattan channel routing  with doglegs allowed  is NPcomplete when all nets have two terminals. This result fills the gap left by Szymanski [Szy85], who showed the NPcompleteness for nets with four terminals. Answering a
Beyond HyperMinimisation—Minimising DBAs and DPAs is NPComplete ∗
"... In this paper we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Büchi, CoBüchi, and parity automata play a similar role in the recognition of ωregular la ..."
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regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic Büchi and parity automata has remained an open challenge. We establish the NPcompleteness of these problems. A second contribution of this paper
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