Related papers: A Graph Minor Perspective to Multicast Network Cod…
A dominating $K_t$ minor in a graph $G$ is a sequence $(T_1,\dots,T_t)$ of pairwise disjoint non-empty connected subgraphs of $G$, such that for $1 \leq i<j\leq t$, every vertex in $T_j$ has a neighbor in $T_i$. Replacing ``every vertex in…
Hadwiger's Conjecture from 1943 states that every graph with chromatic number $t$ contains a $K_t$ minor. Illingworth and Wood [arXiv:2405.14299] introduced the concept of a ``dominating $K_t$ minor'' and asked whether every graph with…
Link and node failures are two common fundamental problems that affect operational networks. Protection of communication networks against such failures is essential for maintaining network reliability and performance. Network protection…
The problem of serving multicast flows in a crossbar switch is considered. Intra-flow linear network coding is shown to achieve a larger rate region than the case without coding. A traffic pattern is presented which is achievable with…
We consider the level of information security provided by random linear network coding in network scenarios in which all nodes comply with the communication protocols yet are assumed to be potential eavesdroppers (i.e. "nice but curious").…
Graph theory has become a very critical component in many applications in the computing field including networking and security. Unfortunately, it is also amongst the most complex topics to understand and apply. In this paper, we review…
Hadwiger's conjecture, among the most famous open problems in graph theory, states that every graph that does not contain $K_t$ as a minor is properly $(t-1)$-colorable. The purpose of this work is to demonstrate that a natural extension of…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process the network nodes collect random subspaces of the…
Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…
The advent of network coding presents promising opportunities in many areas of communication and networking. It has been recently shown that network coding technique can significantly increase the overall throughput of wireless networks by…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
Hadwiger's Conjecture states that every $K_{t+1}$-minor-free graph is $t$-colourable. It is widely considered to be one of the most important conjectures in graph theory. If every $K_{t+1}$-minor-free graph has minimum degree at most…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…