Related papers: The Topology of Local Computing in Networks
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
We summarize the main results proved in recent work on the parameterized verification of safety properties for ad hoc network protocols. We consider a model in which the communication topology of a network is represented as a graph. Nodes…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
A standard model in network synchronised distributed computing is the LOCAL model. In this model, the processors work in rounds and, in the classic setting, they know the number of vertices of the network, $n$. Using $n$, they can compute…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…
Recently a distributed algorithm has been proposed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update…
Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition…
In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
We consider the distributed message-passing {LOCAL} model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
In this paper, we prove topology dependent bounds on the number of rounds needed to compute Functional Aggregate Queries (FAQs) studied by Abo Khamis et al. [PODS 2016] in a synchronous distributed network under the model considered by…
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…