Related papers: Local Partial Clique Covers for Index Coding
The Identifying Code (IC) problem seeks a vertex subset whose intersection with every vertex's closed neighborhood is unique, enabling fault detection in multiprocessor systems and practical uses in identity verification, environmental…
In the Minimum Bisection problem, input is a graph $G$ and the goal is to partition the vertex set into two parts $A$ and $B$, such that $||A|-|B|| \le 1$ and the number $k$ of edges between $A$ and $B$ is minimized. This problem can be…
This work investigates the general two-user Compound Broadcast Channel (BC) where an encoder wishes to transmit common and private messages to two receivers while being oblivious to two possible channel realizations controlling the…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
In this paper, we give simple optimal lower bounds on the one-way two-party communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions. In our model, Alice holds a set of edges and sends a single…
We consider the problem of coding over the multi-user Interference Channel (IC). It is well-known that aligning the interfering signals results in improved achievable rates in certain setups involving more than two users. We argue that in…
In the torn paper channel, a transmitted codeword is broken at random locations into fragments that arrive at the decoder in an unordered manner. A central theoretical challenge within this model is global alignment -- the task of…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…
We develop an improved bound for the chromatic number of graphs of maximum degree $\Delta$ under the assumption that the number of edges spanning any neighbourhood is at most $(1-\sigma)\binom{\Delta}{2}$ for some fixed $0<\sigma<1$. The…
Index coding employs coding across clients within the same broadcast domain. This typically assumes that all clients learn the coding matrix so that they can decode and retrieve their requested data. However, learning the coding matrix can…
One-shot achievable rate region for source coding when coded side information is available at the decoder (source coding with a helper) is proposed. The achievable region proposed is in terms of conditional smooth max Renyi entropy and…
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…
The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…
Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
This paper studies the fundamental limits of the shared-link coded caching problem with correlated files, where a server with a library of $N$ files communicates with $K$ users who can locally cache $M$ files. Given an integer $r \in [N]$,…
The maximum clique problem (MCP) is to find the largest complete subgraph in an undirected graph, that is, the subgraph in which there are edges between every two different vertices. It is an NP-Hard problem with wide applications,…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
A new variant of index coding problem termed as Pliable Index Coding Problem (PICOD) is formulated in [S. Brahma, C. Fragouli, "Pliable index coding", IEEE Transactions on Information Theory, vol. 61, no. 11, pp. 6192-6203, 2015]. In PICOD,…