The Greedy Algorithm for Dissociated Sets
Sayan Dutta

TL;DR
This paper investigates dissociated sets, establishing bounds on their size within initial segments, analyzing the greedy algorithm's behavior, and exploring generalizations, thereby advancing understanding of their structure and construction.
Contribution
It provides new bounds on dissociated sets, proves the greedy algorithm's eventual doubling, and extends results to generalized dissociated sets.
Findings
Bounds on the size of dissociated sets within initial segments.
The greedy algorithm eventually doubles for constructing dissociated sets.
Generalizations of dissociated sets exhibit similar structural properties.
Abstract
A set is said to be a subset-sum-distinct or dissociated if all of its finite subsets have different sums. Alternately, an equivalent classification is if any equality of the form where implies that all the 's are . For a dissociated set , we prove that for and any , we have for all with asymptotic density . Further, we consider the greedy algorithm for generating these sets and prove that this algorithm always eventually doubles. Finally, we also consider some generalizations of dissociated sets and prove similar…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Computability, Logic, AI Algorithms · Complexity and Algorithms in Graphs
