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This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform…
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…
We tackle a stochastic version of the Critical Node Problem (CNP) where the goal is to minimize the pairwise connectivity of a graph by attacking a subset of its nodes. In the stochastic setting considered, the attacks on nodes can fail…
This paper proposes an adaptive transmission algorithm for slotted random access systems supporting the successive interference cancellation (SIC) at the access point (AP). When multiple users transmit packets simultaneously in a slot,…
Given an undirected graph $G$ and a parameter $k$, the $k$-Leaf Spanning Tree ($k$-LST) problem asks if $G$ contains a spanning tree with at least $k$ leaves. This problem has been extensively studied over the past three decades. In 2000,…
In the laminar-constrained spanning tree problem, the goal is to find a minimum-cost spanning tree which respects upper bounds on the number of times each cut in a given laminar family is crossed. This generalizes the well-studied…
We introduce Lumbermark, a robust divisive clustering algorithm capable of detecting clusters of varying sizes, densities, and shapes. Lumbermark iteratively chops off large limbs connected by protruding segments of a dataset's mutual…
Random Linear Network Coding (RLNC) is a transmission scheme that opts for linear combinations of the transmitted packets at a subset of the intermediate nodes. This scheme is usually considered when Network Coding (NC) is desired over…
Random Indexing (RI) K-tree is the combination of two algorithms for clustering. Many large scale problems exist in document clustering. RI K-tree scales well with large inputs due to its low complexity. It also exhibits features that are…
The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using…
Code division multiplexing (CDM)-based random access is used in many practical wireless systems. With CDM-based random access, a set of sequences is reserved for random access. A remote station transmits a random access packet using a…
Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation…
Models for noncoherent error control in random linear network coding (RLNC) and store and forward (SAF) have been recently proposed. In this paper, we model different types of random network communications as the transmission of flats of…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
Wireless networks with many antennas at the base stations and multiplexing of many users, known as Massive MIMO systems, are key to handle the rapid growth of data traffic. As the number of users increases, the random access in contemporary…
This paper proposes Fulcrum network codes, a network coding framework that achieves three seemingly conflicting objectives: (i) to reduce the coding coefficient overhead to almost n bits per packet in a generation of n packets; (ii) to…
We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
This paper proposes and experimentally demonstrates a first wireless local area network (WLAN) system that jointly exploits physical-layer network coding (PNC) and multiuser decoding (MUD) to boost system throughput. We refer to this…
The recent research has established an analogy between successive interference cancellation in slotted ALOHA framework and iterative belief-propagation erasure-decoding, which has opened the possibility to enhance random access protocols by…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…