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Search results for: LOCALLY TREE
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On extremal sizes of locally k-tree graphs
PublicationA graph G is a locally k-tree graph if for any vertex v the subgraph induced by the neighbours of v is a k-tree, k>=0, where 0-tree is an edgeless graph, 1-tree is a tree. We characterize the minimum-size locally k-trees with n vertices. The minimum-size connected locally k-trees are simply (k + 1)-trees. For k >= 1, we construct locally k-trees which are maximal with respect to the spanning subgraph relation. Consequently, the...
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Investigation into MPI All-Reduce Performance in a Distributed Cluster with Consideration of Imbalanced Process Arrival Patterns
PublicationThe paper presents an evaluation of all-reduce collective MPI algorithms for an environment based on a geographically-distributed compute cluster. The testbed was split into two sites: CI TASK in Gdansk University of Technology and ICM in University of Warsaw, located about 300 km from each other, both connected by a fast optical fiber Ethernet-based 100 Gbps network (900 km part of the PIONIER backbone). Each site hosted a set...
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A city is not a tree: a multi-city study on street network and urban life
PublicationChristopher Alexander, a British-American scholar, differentiated an old (natural) city from a new (planned) one by structure. The former resembles a “semilattice”, or a complex system encompassing many interconnected sub-systems. The latter is shaped in a graph-theoretical “tree”, which lacks the structural complexity as its sub-systems are compartmentalized into a single hierarchy. This structural distinction explains why, or...