In this paper, we show a very close relationship between the compaction, vertex-compaction, and retraction problems for reflexive and bipartite graphs. The relationships that we present relate to a long-standing open ...
详细信息
ISBN:
(纸本)9783319788258;9783319788241
In this paper, we show a very close relationship between the compaction, vertex-compaction, and retraction problems for reflexive and bipartite graphs. The relationships that we present relate to a long-standing open problem concerning whether any pair of these problems are polynomially equivalent for every graph. The relationships we present also relate to the constraint satisfaction problem, providing evidence that similar to the compaction and retraction problems, it is also likely to be difficult to give a complete computational complexity classification of the vertex-compaction problem for every reflexive or bipartite graph. In this paper, we however give a complete computational complexity classification of the vertex-compaction problem for all graphs, including even partially reflexive graphs, with four or fewer vertices, by giving proofs based on mostly just knowing the computational complexity classification results of the compaction problem for such graphs determined earlier by the author. Our results show that the compaction, vertex-compaction, and retraction problems are polynomially equivalent for every graph with four or fewer vertices.
According to the Riesz-Markov-Kakutani Representation Theorem and the Lebesgues Decomposition Theorem, every positive (i.e. monotone) linear functionals on the space C[0;1] of continuous functions on the unit interval...
详细信息
Symmetry-based pruning is a family of powerful methods for reducing search effort in planning as heuristic search. Applying these methods requires first establishing an automorphism group that is then used for pruning...
详细信息
Sub-Nyquist sampling based wideband spectrum sensing can usually be summarized as two steps. The first step estimates the signal power spectrum. The second step uses the energy detection method to make a decision. The...
详细信息
In this paper, we consider the solution of the problem of increasing the speed of the algorithm for hyperspectral images (HSI) compression, based on recognition methods. Two methods are proposed to reduce the computat...
详细信息
The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matchin...
详细信息
The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solut...
详细信息
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iter...
详细信息
The present article concerns the theory of the successor function with the unary transitive closure (TC) operator. This theory is equivalent to the TC-theory of discrete linear order with respect to TC-definability. W...
详细信息
This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching ...
详细信息
暂无评论