Related papers: Linear algebraic analogues of the graph isomorphis…
In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…
We investigate the Sherali-Adams lift & project hierarchy applied to a graph isomorphism polytope whose integer points encode the isomorphisms between two graphs. In particular, the Sherali-Adams relaxations characterize a new vertex…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
Havel in 1955, Erd\H{o}s and Gallai in 1960, Hakimi in 1962, Ruskey, Cohen, Eades and Scott in 1994, Barnes and Savage in 1997, Kohnert in 2004, Tripathi, Venugopalan and West in 2010 proposed a method to decide, whether a sequence of…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
Non-adaptive group testing involves grouping arbitrary subsets of $n$ items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
While standard Weisfeiler-Leman vertex labels are not able to distinguish even vertices of regular graphs, there is proposed and tested family of inexpensive polynomial time vertex and edge invariants, distinguishing much more difficult…
By using random multilinear maps, we provide new lower bounds for the Erd\H{o}s box problem, the problem of estimating the extremal number of the complete $d$-partite $d$-uniform hypergraph with two vertices in each part, thereby improving…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
While the P vs NP problem is mainly approached form the point of view of discrete mathematics, this paper proposes reformulations into the field of abstract algebra, geometry, fourier analysis and of continuous global optimization - which…
We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
We consider the problem of deterministically factoring a univariate polynomial over a finite field under the assumption of the Extended Riemann Hypothesis (ERH). This work builds upon the line of approach first explored by Gao in $2001$.…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
It is challenging for generative models to learn a distribution over graphs because of the lack of permutation invariance: nodes may be ordered arbitrarily across graphs, and standard graph alignment is combinatorial and notoriously…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…