A graph is unfrozen with respect to k independent set if it has an independent set of size k after the addition of any edge. The problem of recognizing such graphs is known to be NP-complete. A graph is maximal if the addition of one edge means it is no longer unfrozen. We designate the problem of recognizing maximal unfrozen graphs as MAX(U(k-SET)) and show that this problem is CO-NP-complete....

Let CA be a one-dimensional cellular automaton. A computational complexity problem, the Constrained Eden problem, denoted C-EDEN(CA), is introduced. C-EDEN(CA) is a finitary variant of the Garden of Eden problem. Even for certain elementary cellular automata, C-EDEN(CA) is NP-complete, providing the first examples of NP-complete problems associated with cellular automata over a twoelement alpha...

Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even trivial. A natural step, outstanding thus far, was to provide a broad classification of graphs that make for polynomial or NP-complete instances. We provide...

—Finding a path in a network based on multiple constraints (the MCP problem) is often referred to as QoS routing. QoS routing with constraints on multiple additive metrics has been proven to be NP-complete. This proof has dramatically inßuenced the research community, resulting into the common belief that exact QoS routing is intractable in practice. Hence, many heuristics for this problem were...

Considering the contention for communication resources in task scheduling is discussed in [3]. Theorem 1 of [3] states the NP-completeness of the associated decision problem and the corresponding proof shows NP-completeness in the weak sense [2]. Here, a new proof is presented for Theorem 1 of [3] that shows NP-completeness in the strong sense. The proof is based on a reduction from the well-kn...

This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named " testing problem ". And I get some condition of the NP complete by using testing problem. Second, I make two problem " orderly problem " and " chaotic proble...

The SAT problem being NP-complete, some authors have partitioned its instances in classes described by simple parameters (e.g. the size of a clause). Some of these classes have been shown NP-complete and some polynomial. It is known that the problem of the existence of a solution in a Constraint Network (CN) is NP-complete. But, for CNs having a particular structure (e.g. trees), we know polyno...

– We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the...

The sorting by strip exchanges (aka strip exchanging) problem is motivated by applications in optical character recognition and genome rearrangement analysis. While a couple of approximation algorithms have been designed for the problem, nothing has been known about its computational hardness till date. In this work, we show that the decision version of strip exchanging is NP-Complete. We prese...