Related papers: Detection Performance of M-ary Relay Trees with No…
In this paper, we study beamforming in decode-and-forward (DF) relaying using multiple relays, where the source node sends a secret message as well as a non-secret message to the destination node in the presence of multiple non-colluding…
A recent work shows how we can optimize a tree based mode of operation for a hash function where the sizes of input message blocks and digest are the same, subject to the constraint that the involved tree structure has all its leaves at the…
A $B$-tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2m$ keys for some positive integer $m$, and all leaves have the same distance to the root. We study sequences of $B$-trees that…
Binary LDPC coded relay systems have been well studied previously with the assumption of infinite codeword length. In this paper, we deal with non-binary LDPC codes which can outperform their binary counterpart especially for practical…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…
In this paper we study detection and reconstruction of planted structures in Erd\H{o}s-R\'enyi random graphs. Motivated by a problem of communication security, we focus on planted structures that consist in a tree graph. For planted line…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
Reminiscent of the parity function in network coding for the butterfly network, it is shown that forwarding an even/odd indicator bit for a scalar quantization of a relay observation recovers 1 bit of information at the two destinations in…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
This paper studies the detection and performance analysis problems for a relay network with $N$ parallel decode-and-forward (DF) relays. Due to the distributed nature of this network, it is practically very challenging to fulfill the…
A fringe subtree of a rooted tree is a subtree consisting of one of the nodes and all its descendants. In this paper, we are specifically interested in the number of non-isomorphic trees that appear in the collection of all fringe subtrees…
We present an algorithm for computing a maximum agreement subtree of two unrooted evolutionary trees. It takes O(n^{1.5} log n) time for trees with unbounded degrees, matching the best known time complexity for the rooted case. Our…
Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local…
We address the problem of efficiently gathering correlated data from a wired or a wireless sensor network, with the aim of designing algorithms with provable optimality guarantees, and understanding how close we can get to the known…
A treap is a classic randomized binary search tree data structure that is easy to implement and supports O(\log n) expected time access. However, classic treaps do not take advantage of the input distribution or patterns in the input. Given…
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable…
Trees with many leaves have applications on broadcasting, which is a method in networks for transferring a message to all recipients simultaneously. Internal nodes of a broadcasting tree require more expensive technology, because they have…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We revisit the problem of broadcasting on $d$-ary trees: starting from a Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards its value across binary symmetric channels $\mathrm{BSC}_\delta$ to $d$ descendants. The…