Related papers: An improved Lower Bound for Local Failover in Dire…
Coping with network failures has been recognized as an issue of major importance in terms of social security, stability and prosperity. It has become clear that current networking standards fall short of coping with the complex challenge of…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
We consider wireless networks operating under the SINR model of interference. Nodes have limited individual knowledge and capabilities: they do not know their positions in a coordinate system in the plane, further they do not know their…
Relay networks aid in increasing the rate of communication from source to destination. However, the capacity of even a three-terminal relay channel is an open problem. In this work, we propose a new lower bound for the capacity of the…
A function computation problem in directed acyclic networks has been considered in the literature, where a sink node wants to compute a target function with the inputs generated at multiple source nodes. The network links are error-free but…
We view a neural network as a distributed system of which neurons can fail independently, and we evaluate its robustness in the absence of any (recovery) learning phase. We give tight bounds on the number of neurons that can fail without…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be…
Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…
This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed that only one…
Everyday life is driven by various network, such as supply chains for distributing raw materials, semi-finished product goods, and final products; Internet of Things (IoT) for connecting and exchanging data; utility networks for…
The restoration lemma is a classic result by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [PODC '01], which relates the structure of shortest paths in a graph $G$ before and after some edges in the graph fail. Their work shows that, after…
Local certification is a distributed mechanism enabling the nodes of a network to check the correctness of the current configuration, thanks to small pieces of information called certificates. For many classic global properties, like…
We consider the problem of delivering content cached in a wireless network of n nodes randomly located on a square of area n. The network performance is described by the n2^n-dimensional caching capacity region of the wireless network. We…
In this paper, we consider reachability oracles and reachability preservers for directed graphs/networks prone to edge/node failures. Let $G = (V, E)$ be a directed graph on $n$-nodes, and $P\subseteq V\times V$ be a set of vertex pairs in…
The restoration lemma by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [Dist. Comp. '02] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two…
The optimal fault-tolerance achievable by any protocol has been characterized in a wide range of settings. For example, for state machine replication (SMR) protocols operating in the partially synchronous setting, it is possible to…
The deterministic capacity of a relay network is the capacity of a network when relays are restricted to transmitting \emph{reliable} information, that is, (asymptotically) deterministic function of the source message. In this paper it is…
In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this…