相关论文: On the k-pairs problem

Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which…

We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work…

We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and…

Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…

Recent algorithmic developments have enabled computers to automatically determine and prove the capacity regions of small hypergraph networks under network coding. A structural theory relating network coding problems of different sizes is…

Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…

The algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. This paper investigates the problem of accelerating the convergence of consensus processes by adding links to…

We investigate the achievable rate of data transmission from sources to sinks through a multiple-relay network. We study achievable rates for omniscient coding, in which all nodes are considered in the coding design at each node. We find…

We consider the multiple unicast problem under network coding over directed acyclic networks with unit capacity edges. There is a set of n source-terminal (s_i - t_i) pairs that wish to communicate at unit rate over this network. The…

We consider the problem of selecting $k$ seed nodes in a network to maximize the minimum probability of activation under an independent cascade beginning at these seeds. The motivation is to promote fairness by ensuring that even the least…

The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…

Vertex connectivity and its variants are among the most fundamental problems in graph theory, with decades of extensive study and numerous algorithmic advances. The directed variants of vertex connectivity are usually solved by manually…

We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i-t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the…

We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…

We present a graph theoretic upper bound on speedup needed to achieve 100% throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches - i.e.…

We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing,…

The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…

For minimally $k$-connected graphs on $n$ vertices, Mader proved a tight lower bound for the number $|V_k|$ of vertices of degree $k$ in dependence on $n$ and $k$. Oxley observed 1981 that in many cases a considerably better bound can be…

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…

Node-connectivity augmentation is a fundamental network design problem. We are given a $k$-node connected graph $G$ together with an additional set of links, and the goal is to add a cheap subset of links to $G$ to make it $(k+1)$-node…