DeepAI

# Improved LCAs for constructing spanners

In this paper we study the problem of constructing spanners in a local manner, specifically in the Local Computation Model proposed by Rubinfeld et al. (ICS 2011). We provide an LCA for constructing (2r-1)-spanners with O(n^1+1/r) edges and probe complexity of O(n^1-1/r) r ∈{2,3}, where n denotes the number of vertices in the input graph. Up to polylogarithmic factors, in both cases the stretch factor is optimal (for the respective number of edges). In addition, our probe complexity for r=2, i.e., for constructing 3-spanner is optimal up to polylogarithmic factors. Our result improves over the probe complexity of Parter et al. (ITCS 2019) that is O(n^1-1/2r) for r ∈{2,3}. For general k≥ 1, we provide an LCA for constructing O(k^2)-spanners with Õ(n^1+1/k) edges on expectation whose probe complexity is O(n^2/3Δ^2). This improves over the probe complexity of Parter et al. that is O(n^2/3Δ^4).

• 1 publication
• 7 publications
12/19/2018

### Efficient Representation and Counting of Antipower Factors in Words

A k-antipower (for k > 2) is a concatenation of k pairwise distinct word...
06/09/2019

### Encouraging Paragraph Embeddings to Remember Sentence Identity Improves Classification

While paragraph embedding models are remarkably effective for downstream...
11/14/2022

### SPE: Symmetrical Prompt Enhancement for Fact Probing

Pretrained language models (PLMs) have been shown to accumulate factual ...
02/21/2019

### Local Computation Algorithms for Spanners

A graph spanner is a fundamental graph structure that faithfully preserv...
01/09/2020

### RAC Drawings in Subcubic Area

In this paper, we study tradeoffs between curve complexity and area of R...
09/15/2020

### An information theoretic view on selecting linguistic probes

There is increasing interest in assessing the linguistic knowledge encod...
09/22/2011

### RPA: Probabilistic analysis of probe performance and robust summarization

Probe-level models have led to improved performance in microarray studie...