Efficient Removal Without Efficient Regularity
نویسندگان
چکیده
منابع مشابه
Efficient Removal without Efficient Regularity
Obtaining an efficient bound for the triangle removal lemma is one of the most outstanding open problems of extremal combinatorics. Perhaps the main bottleneck for achieving this goal is that triangle-free graphs can be highly unstructured. For example, triangle-free graphs might have only regular partitions (in the sense of Szemerédi) of tower-type size. And indeed, essentially all the graph p...
متن کاملEfficient Testing without Efficient Regularity
The regularity lemma of Szemerédi turned out to be the most powerful tool for studying the testability of graph properties in the dense graph model. In fact, as we argue in this paper, this lemma can be used in order to prove (essentially) all the previous results in this area. More precisely, a barrier for obtaining an efficient testing algorithm for a graph property P was having an efficient ...
متن کاملEfficient Arithmetic Regularity and Removal Lemmas for Induced Bipartite Patterns
Let G be an abelian group of bounded exponent and A ⊂ G. We show that if the collection of translates of A has VC dimension at most d, then for every > 0 there is a subgroup H of G of index at most −d−o(1) such that one can add or delete at most |G| elements to A to make it a union of H-cosets. We also establish a removal lemma with polynomial bounds, with applications to property testing, for ...
متن کاملAn efficient sparse regularity concept
Let A be a 0/1 matrix of size m × n, and let p be the density of A (i.e., the number of ones divided by m · n). We show that A can be approximated in the cut norm within ε ·mnp by a sum of cut matrices (of rank 1), where the number of summands is independent of the sizem ·n of A, provided that A satisfies a certain boundedness condition. This decomposition can be computed in polynomial time. Th...
متن کاملEfficient Logic Optimization Using Regularity Extraction
This paper presents a new method to extract functionally equivalent structures from logic netlists. It uses a fast functional regularity extraction algorithm based on structural equivalence. The goal of the proposed algorithm is the speedup of logic optimization of large circuits by reusing functionally equivalent structures of the design. It is particularly suited for circuits containing a lar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorica
سال: 2019
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-018-3899-6