Research on Spatial and Dynamic Planning Methods for Settlement Buildings Based on Data Mining

Traditional settlements are widely concerned by academic circles for their unique settlement patterns, exquisite residential buildings, and rich historical and cultural connotations, and their protection and development is an important proposition for rural revitalization. Therefore, from the perspective of big data mining (BDM), this paper explores its application in architectural space and settlement protection of traditional settlements in Hainan and provides new ideas for the protection and renewal of traditional settlements in Hainan. The attribute elements of spatial data of settlement groups are analyzed by the decision tree classification mining method. In order to avoid the multivalued tendency of ID3 algorithm and improve the efficiency of decision tree generation by ID3 algorithm, an improved ID3 algorithm is proposed by introducing user interest and simplifying the calculation process of the algorithm. At the same time, the graph theory recognition method of grid pattern is proposed. Aiming at the intersection graph and direction relation graph of straight line pattern, grid pattern recognition is realized by solving the connectivity, intersection, and subsequent construction of the maximum complete subgraph. Experiments show that the improved ID3 algorithm has better running efficiency than the parallel algorithm based on cooccurrence matrix. The analysis of the architectural space of traditional settlements in Hainan will help us better grasp social activities and provide direction for the protection and renewal of traditional settlements from the perspective of tourists and residents.

On-line interval graphs coloring — Modification of the First-Fit algorithm and its performance ratio

We propose a modification of the First-Fit algorithm in which we forbid the use of the most frequently used color. We provide some lower bound of the performance ratio [Formula: see text] on the family of interval graphs [Formula: see text], where [Formula: see text] denotes the number of used colors by the modified version of the First-Fit algorithm and [Formula: see text] is the number of vertices in the largest complete subgraph in [Formula: see text]. We also compare the modification with the usual First-Fit algorithm on some experimental data.

Optimization of data allocation in hierarchical memory for blocked shortest paths algorithms

This paper is devoted to the reduction of data transfer between the main memory and direct mapped cache for blocked shortest paths algorithms (BSPA), which represent data by a D[M×M] matrix of blocks. For large graphs, the cache size S = δ×M2, δ < 1 is smaller than the matrix size. The cache assigns a group of main memory blocks to a single cache block. BSPA performs multiple recalculations of a block over one or two other blocks and may access up to three blocks simultaneously. If the blocks are assigned to the same cache block, conflicts occur among the blocks, which imply active transfer of data between memory levels. The distribution of blocks on groups and the block conflict count strongly depends on the allocation and ordering of the matrix blocks in main memory. To solve the problem of optimal block allocation, the paper introduces a block conflict weighted graph and recognizes two cases of block mapping: non-conflict and minimum-conflict. In first case, it formulates an equitable color-class-size constrained coloring problem on the conflict graph and solves it by developing deterministic and random algorithms. In second case, the paper formulates a problem of weighted defective color-count constrained coloring of the conflict graph and solves it by developing a random algorithm. Experimental results show that the equitable random algorithm provides an upper bound of the cache size that is very close to the lower bound estimated over the size of a complete subgraph, and show that a non-conflict matrix allocation is possible at δ = 0.5 for M = 4 and at δ = 0.1 for M = 20. For a low cache size, the weighted defective algorithm gives the number of remaining conflicts that is up to 8.8 times less than the original BSPA gives. The proposed model and algorithms are applicable to set-associative cache as well.

Discovering the maximum k-clique on social networks using bat optimization algorithm

The k-clique problem is identifying the largest complete subgraph of size k on a network, and it has many applications in Social Network Analysis (SNA), coding theory, geometry, etc. Due to the NP-Complete nature of the problem, the meta-heuristic approaches have raised the interest of the researchers and some algorithms are developed. In this paper, a new algorithm based on the Bat optimization approach is developed for finding the maximum k-clique on a social network to increase the convergence speed and evaluation criteria such as Precision, Recall, and F1-score. The proposed algorithm is simulated in Matlab® software over Dolphin social network and DIMACS dataset for k = 3, 4, 5. The computational results show that the convergence speed on the former dataset is increased in comparison with the Genetic Algorithm (GA) and Ant Colony Optimization (ACO) approaches. Besides, the evaluation criteria are also modified on the latter dataset and the F1-score is obtained as 100% for k = 5.

Alternative Branching Strategies in the Branch and Bound Algorithm by Using a K-Clique Covering Vertex Set for Maximum Clique Problems

The maximum clique problem (MCP) is graph theory problem that demand complete subgraph with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm. In this paper, we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarantee finding maximum clique.

Improved bounds for the Erdős-Rogers function

[Ramsey's Theorem](https://en.wikipedia.org/wiki/Ramsey%27s_theorem) is one of the most prominent results in graph theory. In its simplest form, it asserts that every sufficiently large two-edge-colored complete graph contains a large monochromatic complete subgraph. This theorem has been generalized to a plethora of statements asserting that every sufficiently large structure of a given kind contains a large "tame" substructure. The article concerns a closely related problem: for a structure with a given property, find a substructure possessing an even stronger property. For example, what is the largest $K_3$-free induced subgraph of an $n$-vertex $K_4$-free graph? The answer to this question is approximately $n^{1/2}$. The lower bound is easy. If a given graph has a vertex of degree at least $n^{1/2}$, then its neighbors induce a $K_3$-free subgraph with at least $n^{1/2}$ vertices. Otherwise, a greedy procedure yields an independent set of size almost $n^{1/2}$. The argument generalizes to $K_s$-free induced subgraphs of $K_{s+1}$-free graphs. Dudek, Retter and Rödl provided a construction showing that the exponent $1/2$ cannot be improved and asked whether the same is the case for $K_s$-free induced subgraphs of $K_{s+2}$-free graphs. The authors answer this question by providing a construction of $K_{s+2}$-free $n$-vertex graphs with no $K_s$-free induced subgraph with $n^{\alpha_s}$ vertices with $\alpha_s<1/2$ for every $s\ge 3$. Their arguments extend to the case of $K_t$-free graphs with no large $K_s$-free induced subgraph for $s+2\le t\le 2s-1$ and $s\ge 3$.

Detecting overlapping protein complexes in weighted PPI network based on overlay network chain in quotient space

Background Protein complexes are the cornerstones of many biological processes and gather them to form various types of molecular machinery that perform a vast array of biological functions. In fact, a protein may belong to multiple protein complexes. Most existing protein complex detection algorithms cannot reflect overlapping protein complexes. To solve this problem, a novel overlapping protein complexes identification algorithm is proposed. Results In this paper, a new clustering algorithm based on overlay network chain in quotient space, marked as ONCQS, was proposed to detect overlapping protein complexes in weighted PPI networks. In the quotient space, a multilevel overlay network is constructed by using the maximal complete subgraph to mine overlapping protein complexes. The GO annotation data is used to weight the PPI network. According to the compatibility relation, the overlay network chain in quotient space was calculated. The protein complexes are contained in the last level of the overlay network. The experiments were carried out on four PPI databases, and compared ONCQS with five other state-of-the-art methods in the identification of protein complexes. Conclusions We have applied ONCQS to four PPI databases DIP, Gavin, Krogan and MIPS, the results show that it is superior to other five existing algorithms MCODE, MCL, CORE, ClusterONE and COACH in detecting overlapping protein complexes.

The Ramsey number of books

Ramsey's Theorem is among the most well-known results in combinatorics. The theorem states that any two-edge-coloring of a sufficiently large complete graph contains a large monochromatic complete subgraph. Indeed, any two-edge-coloring of a complete graph with N=4t−o(t) vertices contains a monochromatic copy of Kt. On the other hand, a probabilistic argument yields that there exists a two-edge-coloring of a complete graph with N=2t/2+o(t) with no monochromatic copy of Kt. Much attention has been paid to improving these classical bounds but only improvements to lower order terms have been obtained so far. A natural question in this setting is to ask whether every two-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of Kt that can be extended in many ways to a monochromatic copy of Kt+1. Specifically, Erdős, Faudree, Rousseau and Schelp in the 1970's asked whether every two-edge-coloring of KN contains a monochromatic copy of Kt that can be extended in at least (1−ok(1))2−tN ways to a monochromatic copy of Kt+1. A random two-edge-coloring of KN witnesses that this would be best possible. While the intuition coming from random constructions can be misleading, for example, a famous construction by Thomason shows the existence of a two-edge-coloring of a complete graph with fewer monochromatic copies of Kt than a random two-edge-coloring, this paper confirms that the intuition coming from a random construction is correct in this case. In particular, the author answers this question of Erdős et al. in the affirmative. The question can be phrased in the language of Ramsey theory as a problem on determining the Ramsey number of book graphs. A book graph B(k)t is a graph obtained from Kt by adding k new vertices and joining each new vertex to all the vertices of Kt. The main result of the paper asserts that every two-edge-coloring of a complete graph with N=2kt+ok(t) vertices contains a monochromatic copy of B(k)t.