Related papers: Network Coding for $3$s$/n$t Sum-Networks
Linial's seminal result shows that any deterministic distributed algorithm that finds a $3$-colouring of an $n$-cycle requires at least $\log^*(n)/2 - 1$ communication rounds. We give a new simpler proof of this theorem.
The decode-forward achievable region is studied for general networks. The region is subject to a fundamental tension in which nodes individually benefit at the expense of others. The complexity of the region depends on all the ways of…
We address the problem of increasing the sum rate in a multiple-access system from [1] for small number of users. We suggest an improved signal-code construction in which in case of a small number of users we give more resources to them.…
We study the growth of networks from a set of isolated ground nodes by the addition of one new node per time step and also of a fixed number of directed edges leading from the new node to randomly selected nodes already in the network. A…
We develop an abstract axiomatic theory of tie-breaking. A tie-breaking input consists of a finite set N of players, a weak order on N representing the standings to be refined, and an auxiliary information item drawn from a set on which the…
The 2008 financial crisis has been attributed to "excessive complexity" of the financial system due to financial innovation. We employ computational complexity theory to make this notion precise. Specifically, we consider the problem of…
Given a set of $n$ real numbers, the 3SUM problem is to decide whether there are three of them that sum to zero. Until a recent breakthrough by Gr{\o}nlund and Pettie [FOCS'14], a simple $\Theta(n^2)$-time deterministic algorithm for this…
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 define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…
Consider the following information theoretic setup wherein independent codebooks of N correlated random variables are generated according to their respective marginals. The problem of determining the conditions on the rates of codebooks to…
Many emerging multimedia streaming applications involve multiple users communicating under strict latency constraints. In this paper we study streaming codes for a network involving two source nodes, one relay node and a destination node.…
This paper considers a massive connectivity setting in which a base-station (BS) aims to communicate sources $(X_1,\cdots,X_k)$ to a randomly activated subset of $k$ users, among a large pool of $n$ users, via a common message in the…
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…
Sum-rank codes have known applications in the multishot network coding, the distributed storage and the construction of space-time codes. U. Mart\'{\i}nez-Pe\~{n}as introduced the cyclic-skew-cyclic sum-rank codes and proposed the BCH bound…
In this paper, we study crucial elements of a complex network, namely its nodes and connections, which play a key role in maintaining the network's structure and function under unexpected structural perturbations of nodes and edges removal.…
We present a case for the use of codes possessing algebraic closure properties - coset codes - in developing coding techniques and characterizing achievable rate regions for generic multi-terminal channels. In particular, we consider three…
The question of how and why the phenomenon of mode connectivity occurs in training deep neural networks has gained remarkable attention in the research community. From a theoretical perspective, two possible explanations have been proposed:…
Entanglement is a complexity measure of digraphs that origins in fixed-point logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs. We address the problem of characterizing the structure of graphs of…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
Coupled cell systems associated with a coupled cell network are determined by (smooth) vector fields that are consistent with the network structure. Here, we follow the formalisms of Stewart, Golubitsky and Pivato (Symmetry groupoids and…