Related papers: High-rate storage codes on triangle-free graphs
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…
We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V|)+1 where V is the set of vertices of the graph.…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…
Graph partitioning (GP) and vertex connectivity have traditionally been two distinct fields of study. This paper introduces the highly connected graph partitioning (HCGP) problem, which partitions a graph into compact, size balanced, and…
In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…
Recently a powerful class of rate-compatible serially concatenated convolutional codes (SCCCs) have been proposed based on minimizing analytical upper bounds on the error probability in the error floor region. Here this class of codes is…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.)…
Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…
We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs,…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
We address the problem of distributed computation of arbitrary functions of two correlated sources $X_1$ and $X_2$, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
We construct a hereditary class of triangle-free graphs with unbounded chromatic number, in which every non-trivial graph either contains a pair of non-adjacent twins or has an edgeless vertex cutset of size at most two. This answers in the…
Approximate nearest neighbor search for vectors relies on indexes that are most often accessed from RAM. Therefore, storage is the factor limiting the size of the database that can be served from a machine. Lossy vector compression, i.e.,…
In line with the recent development in topological graph theory, we are considering undirected graphs that are allowed to contain {\em multiple edges}, {\em loops}, and {\em semi-edges}. A graph is called {\em simple} if it contains no…
Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…