Steiner Minimal Tree Algorithm Research Articles

Network Analysis of Osteoarthritis Progression Using a Steiner Minimal Tree Algorithm.

To provide a comprehensive analysis of associated genes with osteoarthritis (OA). Here, we reported a network analysis of OA progression by using a Steiner minimal tree algorithm. We collected the OA-related genes through screening the publications in MEDLINE. We performed functional analysis to analyze the associated biochemical pathways of the OA-related genes. Pathway crosstalk analysis was constructed to explore interactions of the enriched pathways. Steiner minimal tree algorithm was used to analyze molecular pathway networks. The average clustering coefficient was compared with the corresponding values of the Osteoarthritis-specific network. The new finding RNA was compared with former single-cell RNA-seq analysis results. A gene set with 177 members reported to be significantly associated with Osteoarthritis was collected from 187 studies. Functional enrichment analysis revealed a specific related-OA gene including skeletal system development, cytokine-mediated signaling pathway, inflammatory response, cartilage development, and extracellular matrix organization. We performed a pathway crosstalk analysis among the 72 significantly enriched pathways. A total of 151 of the 177 genes in the Osteoarthritis gene set were included in the human interactome network. There were 31 genes in the former single-cell RNA-seq analysis results. The CLU, ENO1, SRRM1, UBC, HMGB1, NR3C1, NOTCH2NL, and CBX5 have significantly increased expression in seven molecularly defined populations of OA cartilage. The Steiner tree-based approach finds new biological molecules associated with OA genes.

Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

In this paper, we present a parallel 2-approximation Steiner minimal tree algorithm and its MPI-based distributed implementation. In place of expensive distance computations between all pairs of seed vertices, the solution we employ exploits a cheaper Voronoi cell computation. Our design leverages asynchronous processing and message prioritization to accelerate convergence of distance computations, and harnesses vertex and edge centric processing to offer fast time-to-solution. We demonstrate scalability and performance using real-world graphs with up to 128 billion edges and 512 compute nodes, and show the ability to find Steiner trees with up to one million seed vertices. Using 12 data instances, we present comparison with the state-of-the-art exact solver, SCIP-Jack, and two sequential 2-approximate algorithms. We empirically show that, on average, the total distance of the Steiner tree identified by our solution is 1.1290 times greater than the Steiner minimal tree – well within the theoretical approximation bound of 2.

Identification of genes associated with sudden cardiac death: a network- and pathway-based approach.

BackgroundSudden cardiac death (SCD) accounts for a large proportion of the total deaths across different age groups. Although numerous candidate genes related to SCD have been identified by genetic association studies and genome wide association studies (GWAS), the molecular mechanisms underlying SCD are still unclear, and the biological functions and interactions of these genes remain obscure. To clarify this issue, we performed a comprehensive and systematic analysis of SCD-related genes by a network and pathway-based approach.MethodsBy screening the publications deposited in the PubMed and Gene-Cloud Biotechnology Information (GCBI) databases, we collected the genes genetically associated with SCD, which were referred to as the SCD-related gene set (SCDgset). To analyze the biological processes and biochemical pathways of the SCD-related genes, functional analysis was performed. To explore interlinks and interactions of the enriched pathways, pathway crosstalk analysis was implemented. To construct SCD-specific molecular networks, Markov cluster algorithm and Steiner minimal tree algorithm were employed.ResultsWe collected 257 genes that were reported to be associated with SCD and summarized them in the SCDgset. Most of the biological processes and biochemical pathways were related to heart diseases, while some of the biological functions may be noncardiac causes of SCD. The enriched pathways could be roughly grouped into two modules. One module was related to calcium signaling pathway and the other was related to MAPK pathway. Moreover, two different SCD-specific molecular networks were inferred, and 23 novel genes potentially associated with SCD were also identified.ConclusionsIn summary, by means of a network and pathway-based methodology, we explored the pathogenetic mechanism underlying SCD. Our results provide valuable information in understanding the pathogenesis of SCD and include novel biomarkers for diagnosing potential patients with heart diseases; these may help in reducing the corresponding risks and even aid in preventing SCD.

X-architecture Steiner minimal tree algorithm based on multi-strategy optimization discrete differential evolution.

Global routing is an important link in very large scale integration (VLSI) design. As the best model of global routing, X-architecture Steiner minimal tree (XSMT) has a good performance in wire length optimization. XSMT belongs to non-Manhattan structural model, and its construction process cannot be completed in polynomial time, so the generation of XSMT is an NP hard problem. In this paper, an X-architecture Steiner minimal tree algorithm based on multi-strategy optimization discrete differential evolution (XSMT-MoDDE) is proposed. Firstly, an effective encoding strategy, a fitness function of XSMT, and an initialization strategy of population are proposed to record the structure of XSMT, evaluate the cost of XSMT and obtain better initial particles, respectively. Secondly, elite selection and cloning strategy, multiple mutation strategies, and adaptive learning factor strategy are presented to improve the search process of discrete differential evolution algorithm. Thirdly, an effective refining strategy is proposed to further improve the quality of the final Steiner tree. Finally, the results of the comparative experiments prove that XSMT-MoDDE can get the shortest wire length so far, and achieve a better optimization degree in the larger-scale problem.

Performance analysis of multilayer multicast MANET CRN based on steiner minimal tree algorithm

In this study, the multicast mobile ad hoc (MANET) CRN has been developed, which involves multi-hop and multilayer consideration and Steiner minimal tree (SMT) algorithm is employed as the router protocol. To enhance the network performance with regards to throughput and packet delivery rate (PDR), as channel assignment scheme, the probability of success (POS) is employed that accounts for the channel availability and the time needed for transmission when selecting the best channel from the numerous available channels for data transmission from the source to all destinations nodes effectively. Within Rayleigh fading channels under various network parameters, a comparison is done for the performance of SMT multicast (MANET) CRN with POS scheme versus maximum data rate (MDR), maximum average spectrum availability (MASA) and random channel assignment schemes. Based on the simulation results, the SMT multicast (MANET) CRN with POS scheme was seen to demonstrate the best performance versus other schemes. Also the results proved that the throughput and PDR performance are improved as the number the primary channels and the channel’s bandwidth increased while dropped as the value of packet size D increased. The network’s performance grew with rise in the value of idle probability (P_I) since the primary user’s (PU) traffic load is low when the value of P_I is high.

Performance comparison of multicast MANET CRN system’s based on POS scheme with different types of router protocol algorithms

<p>A multi-layer multi-hop mechanism, with one of three different types of router protocol algorithms (Steiner minimal tree (SMT), shortest path tree (SPT) and minimal spanning tree (MST)) was employed for the construction of multi-cast MANET CRNs. The probability of success (POS) used as the channel assignment scheme, is dependent on the availability of the channel, and the required transmission time. It was applied to the network after the conversion of the network’s random topology into one of the three algorithms (SMT, SPT or MST). This facilitated the selection of an efficient channel for the transmission of the CR user’s data, under the effect of the Rayleigh fading channel. Three idle probability circumstances (i.e., =0.1, 0.5, 0.9), and different network parameters, were used to compare the performance of the CRN with three routing protocols in terms of throughput, and packet delivery rate (PDR). According to the simulation results, for a high traffic load of PUs ( 1) at different network parameters , the CRN with the SPT algorithm performed better than the CRN with the SMT or MST algorithm. </p>

Network and Pathway-Based Analyses of Genes Associated with Parkinson's Disease.

Parkinson's disease (PD) is a major neurodegenerative disease influenced by both genetic and environmental factors. Although previous studies have provided insights into the significant impacts of genetic factors on PD, the molecular mechanism underlying PD remains largely unclear. Under such situation, a comprehensive analysis focusing on biological function and interactions of PD-related genes will provide us valuable information to understand the pathogenesis of PD. In the current study, by reviewing the literatures deposited in PUBMED, we identified 242 genes genetically associated with PD, referred to as PD-related genes gene set (PDgset). Functional analysis revealed that biological processes and biochemical pathways related to neurodevelopment, metabolism, and immune system were enriched in PDgset. Then, pathway crosstalk analysis indicated that the enriched pathways could be grouped into two modules, with one module consisted of pathways mainly involved in neuronal signaling and another in immune response. Further, based on a global human interactome, we found that PDgset tended to have more moderate degree compared with cancer-related genes. Moreover, PD-specific molecular network was inferred using Steiner minimal tree algorithm and some potential related genes associated with PD were identified. In summary, by using network- and pathway-based methods to explore pathogenetic mechanism underlying PD, results from our work may have important implications for understanding the molecular mechanism underlying PD. Also, the framework proposed in our current work can be used to infer pathological molecular network and genes related to a specific disease.

FOARS: FLUTE Based Obstacle-Avoiding Rectilinear Steiner Tree Construction

In this paper, we present an algorithm called FOARS for obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction. FOARS applies a top-down approach which first partitions the set of pins into several subsets uncluttered by obstacles. Then an obstacle-avoiding Steiner tree is generated for each subset by an obstacle aware version of the rectilinear Steiner minimal tree algorithm FLUTE. Finally, the trees are merged and refined to form the OARSMT. To guide the partitioning of pins, we propose a novel algorithm to construct a linear-sized obstacle-avoiding spanning graph which guarantees to contain a rectilinear minimum spanning tree if there is no obstacle. Experimental results show that FOARS is among the best algorithms in terms of both wirelength and runtime for testcases both with and without obstacles.

Efficient Steiner Tree Construction Based on Spanning Graphs

The Steiner Minimal Tree (SMT) problem is a very important problem in very large scale integrated computer-aided design. Given n points on a plane, an SMT connects these points through some extra points (called Steiner points) to achieve a minimal total length. Even though there exist many heuristic algorithms for this problem, they have either poor performances or expensive running time. This paper records an implementation of an efficient SMT algorithm that has a worst case running time of O(nlogn) and a performance close to that of the Iterated 1-Steiner algorithm. The algorithm efficiently combines Borah et al.'s edge substitute concept with Zhou et al.'s spanning graph. Extensive experimental studies are conducted to compare it with other programs.