Domingos Dellamonica

An Exact Algorithm for Optimal MAE Stack Filter Design

We propose a new algorithm for optimal MAE stack filter design. It is based on three main ingredients. First, we show that the dual of the integer programming formulation of the filter design problem is a minimum cost network flow problem. Next, we present a decomposition principle that can be used to break this dual problem into smaller subproblems. Finally, we propose a specialization of the network Simplex algorithm based on column generation to solve these smaller subproblems. Using our method, we were able to efficiently solve instances of the filter problem with window size up to 25 pixels. To the best of our knowledge, this is the largest dimension for which this problem was ever solved exactly

Universality of Random Graphs

We prove that asymptotically (as <i>n</i> → ∞) almost all graphs with <i>n</i> vertices and 10<i>d n</i>²--1/2<i>d</i> log ^1/<i>d</i> <i>n</i> edges are universal with respect to the family of all graphs with maximum degree bounded by <i>d.</i> Moreover, we provide a polynomial time, deterministic embedding algorithm to find a copy of each bounded degree graph in every graph satisfying some pseudo-random properties. We also prove a counterpart result for random bipartite graphs, where the threshold number of edges is even smaller but the embedding is randomized.

A Deterministic Algorithm for the Frieze-Kannan Regularity Lemma

The Frieze-Kannan regularity lemma is a powerful tool in combinatorics. It has also found applications in the design of approximation algorithms and recently in the design of fast combinatorial algorithms for boolean matrix multiplication. The algorithmic applications of this lemma require one to efficiently construct a partition satisfying the conditions of the lemma. R. Williams recently asked if one can construct a partition satisfying the conditions of the Frieze-Kannan regularity lemma in deterministic subcubic time. We resolve this problem by designing an

An Optimal Algorithm for Finding Frieze-Kannan Regular Partitions

\tilde O(n^{\omega})

Hereditary quasirandom properties of hypergraphs

time algorithm for constructing such a partition, where

The number of B3-sets of a given cardinality

\omega < 2.376

The size‐Ramsey number of trees

is the exponent of fast matrix multiplication. The algorithm relies on a spectral characterization of vertex partitions satisfying the properties of the Frieze-Kannan regularity lemma.

On a conjecture of Thomassen concerning subgraphs of large girth

In this paper we prove that two local conditions involving the degrees and co-degrees in a graph can be used to determine whether a given vertex partition is Frieze{Kannan-regular. With a more rened version of these two local conditions we provide a deterministic algorithm that obtains a Frieze{Kanan-regular partition of any graph G in time O(jV (G)j 2 ).

An algorithmic Friedman--Pippenger theorem on tree embeddings and applications to routing

Thomason and Chung, Graham and Wilson were the first to systematically investigate properties of quasirandom graphs. They have stated several quite disparate graph properties — such as having uniform edge distribution or containing a prescribed number of certain subgraphs — and proved that these properties are equivalent in a deterministic sense.Simonovits and Sós introduced a hereditary property (which we call S) stating the following: for a small fixed graph L, a graph G on n vertices is said to have the property S if for every set X ⊆ V(G), the number of labeled copies of L in G[X] (the subgraph of G induced by the vertices of X) is given by 2−e(L)|X|υ(L) + o(nυ(L)). They have shown that S is equivalent to the other quasirandom properties.In this paper we give a natural extension of the result of Simonovits and Sós to k-uniform hypergraphs, answering a question of Conlon et al. Our approach also yields an alternative, and perhaps simpler, proof of one of their theorems.

Distance preserving ramsey graphs

A set S of integers is a B 3 -set if all the sums of the form a 1 + a 2 + a 3 , with a 1 , a 2 and a 3 ? S and a 1 ? a 2 ? a 3 , are distinct. We obtain asymptotic bounds for the number of B 3 -sets of a given cardinality contained in the interval n = { 1 , ? , n } . We use these results to estimate the maximum size of a B 3 -set contained in a typical (random) subset of n of a given cardinality. These results confirm conjectures recently put forward by the authors On the number of B h -sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127.