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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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Shellings from Relative Shellings, with an Application to NP-Completeness
Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large...
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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 the Independent Dominating Set Problem in the Class of Cubic Planar Bipartite Graphs
AbstractIt is known that the independent dominating set problem is NP-complete both in the class of cubic planar graphs and in the class of cubic...
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NP-completeness of optimal planning problem for modular robots
Self-reconfigurable modular robots (SRM-robots) can autonomously change their shape according to different tasks and work environments, and have...
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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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Maximum Cut on Interval Graphs of Interval Count Four is NP-Complete
The computational complexity of the MaxCut problem restricted to interval graphs has been open since the 80’s, being one of the problems proposed by...
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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 and Algorithms for Domination in Graphs
In this chapter,we provide an overviewof some of the core results on NP-completeness and algorithms for domination, independent domination, and total...
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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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Excessive interstitial free-water in cortical gray matter preceding accelerated volume changes in individuals at clinical high risk for psychosis
Recent studies show that accelerated cortical gray matter (GM) volume reduction seen in anatomical MRI can help distinguish between individuals 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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Counting on Rainbow k-Connections
For an undirected graph imbued with an edge coloring, a rainbow path (resp. proper path) between a pair of vertices corresponds to a simple path in...
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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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Complexity Analysis
This Chapter advocates a structure-oriented approach to simplify and generalize complexity investigations. The DIAGONALIZATION and REDUCTION methods...