Related papers: New constructions for covering designs
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…
An $(n,R)$-covering sequence is a cyclic sequence whose consecutive $n$-tuples form a code of length $n$ and covering radius $R$. Using several construction methods improvements of the upper bounds on the length of such sequences for $n…
In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
A basic problem for the constant dimension subspace coding is to determine the maximal possible size A_q (n, d, k) of a set of k-dimensional subspaces in Fnq such that the subspace distance satisfies d(U, V )> or =d for any two different…
Let $\mathcal D=(\Omega, \mathcal B)$ be a pair of $v$ point set $\Omega$ and a set $\mathcal B$ consists of $k$ point subsets of $\Omega$ which are called blocks. Let $d$ be the maximal cardinality of the intersections between the distinct…
In this work, constructions of ordered covering arrays are discussed and applied to obtain new upper bounds on covering codes in Rosenbloom-Tsfasman spaces (RT spaces), improving or extending some previous results.
We investigate {\em multidimensional covering mechanism-design} problems, wherein there are $m$ items that need to be covered and $n$ agents who provide covering objects, with each agent $i$ having a private cost for the covering objects he…
Constant-dimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although…
Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…
In any attempt at designing an efficient algorithm for the minimum vertex cover problem, obtaining good upper and lower bounds for the vertex cover number could be crucial. In this article we present a modified greedy algorithm of…
Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…
A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to…
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…
We revisit the classic Maximum $k$-Coverage problem: Determine the largest number $t$ of elements that can be covered by choosing $k$ sets from a given family $\mathcal{F} = \{S_1,\dots, S_n\}$ of a size-$u$ universe. A notable special case…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
We introduce the batched set cover problem, which is a generalization of the online set cover problem. In this problem, the elements of the ground set that need to be covered arrive in batches. Our main technical contribution is a tight…
A $(v,k,t)$ packing of size $b$ is a system of $b$ subsets (blocks) of a $v$-element underlying set such that each block has $k$ elements and every $t$-set is contained in at most one block. $P(v,k,t)$ stands for the maximum possible $b$. A…
Given a $k$-uniform hyper-graph, the E$k$-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to…