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NP- and PSPACE-Completeness
We introduce NP-completeness. We prove the Cook-Levin Theorem. Using it we prove many natural problems are NP-complete, and using similar ideas show...
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Nonuniform Reductions and NP-Completeness
Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions...
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NP-Completeness of the Minimum Spanning Tree Problem of a Multiple Graph of Multiplicity k ≥ 3
Undirected multiple graphs of any natural multiplicity k > 1 are studied. There are edges of three types: ordinary edges, multiple edges, and...
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NP-Completeness and One Polynomial Subclass of the Two-Step Graph Colouring Problem
AbstractThis paper considers the two-step colouring problem for an undirected connected graph. The problem is about colouring the graph in a given...
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NP-Completeness
I will now introduce techniques for proving that no ffcient algorithm can exist for a given problem. The practical reader is probably squirming at...
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NP-completeness of chromatic orthogonal art gallery problem
The chromatic orthogonal art gallery problem is a well-known problem in the computational geometry. Two points in an orthogonal polygon P see each...
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A Physical Zero-Knowledge Proof for Sumplete, a Puzzle Generated by ChatGPT
In March 2023, ChatGPT generated a new puzzle, Sumplete. Sumplete consists of an...
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Complexity of the (Connected) Cluster Vertex Deletion Problem on H-free Graphs
The well-known Cluster Vertex Deletion problem ( cluster-vd ) asks for a given graph G and an integer k whether it is possible to delete a set S of at...
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On the Routing Problems in Graphs with Ordered Forbidden Transitions
Finding a path between two vertices of a given graph is one of the most classic problems in graph theory. Recently, problems of finding a route...
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Finding Optimal Solutions with Neighborly Help
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighbor instances, that is, instances with one...
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Your Reputation’s Safe with Me: Framing-Free Distributed Zero-Knowledge Proofs
Distributed Zero-Knowledge (dZK) proofs, recently introduced by Boneh et al. (CRYPTO‘19), allow a prover...
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The Complexity Classes of Hamming Distance Recoverable Robust Problems
The well-known complexity class NP contains combinatorial problems, whose optimization counterparts are important for many practical settings. In...
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Complexity Analysis
This Chapter advocates a structure-oriented approach to simplify and generalize complexity investigations. The DIAGONALIZATION and REDUCTION methods...
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Recognizing DAGs with Page-Number 2 Is NP-complete
The page-number of a directed acyclic graph (a DAG, for short) is the minimum k for which the DAG has a topological order and a k-coloring of its...
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Splitting Plane Graphs to Outerplanarity
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph...
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Upward and Orthogonal Planarity are W[1]-Hard Parameterized by Treewidth
Upward planarity testing and Rectilinear planarity testing are central problems in graph drawing. It is known that they are both...
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On Star Partition of Split Graphs
A graph that is isomorphic to \(K_{1,r}\) for...
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Stability and Welfare in (Dichotomous) Hedonic Diversity Games
In a hedonic diversity game (HDG) there are two types of agents (red and blue agents) that need to form disjoint coalitions, i.e., subgroups of...
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Hardness of Deceptive Certificate Selection
Recent progress towards theoretical interpretability guarantees for AI has been made with classifiers that are based on interactive proof systems. A...
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Complexity of Reachability Problems in Neural Networks
In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such...