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Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
In this letter, we propose a new routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called {\it…
In Path Integral control problems a representation of an optimally controlled dynamical system can be formally computed and serve as a guidepost to learn a parametrized policy. The Path Integral Cross-Entropy (PICE) method tries to exploit…
In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., $n$ nodes are placed uniformly at random in a square region of area $n$). They…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
The cycle prefix network is a Cayley coset digraph based on sequences over an alphabet which has been proposed as a vertex symmetric communication network. This network has been shown to have many remarkable communication properties such as…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
Mixture-of-Experts (MoE) layers scale transformers by routing tokens to a sparse subset of feed-forward experts. Token-level routing, however, assigns an entire semantic spectrum to each expert, creating capacity bottlenecks, load-balancing…
Geocast is the concept of sending data packets to nodes in a specified geographical area instead of nodes with a specific address. To route geocast messages to their destination we need a geographic routing algorithm that can route packets…
On the one hand, the correctness of routing protocols in networks is an issue of utmost importance for guaranteeing the delivery of messages from any source to any target. On the other hand, a large collection of routing schemes have been…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
The coupling of scale-free networks with mobile unstructured networks is certainly unusual. In mobile networks, connections active at a given instant are constrained by the geographical distribution of mobile nodes, and by the limited…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
Several studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces,…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
Reduction of end-to-end network delays is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for…
We consider several basic questions on distributed routing in directed graphs with multiple additive costs, or metrics, and multiple constraints. Distributed routing in this sense is used in several protocols, such as IS-IS and OSPF. A…
Network alignment is the task of establishing one-to-one correspondences between the nodes of different graphs. Although finding a plethora of applications in high-impact domains, this task is known to be NP-hard in its general form.…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…