Related papers: A Note on the Parallel Cleaning of Cliques
This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph and no two jobs connected by an edge are allowed to be assigned to the same machine. In particular, we study the case where the…
Contrastive learning (CL) recently has spurred a fruitful line of research in the field of recommendation, since its ability to extract self-supervised signals from the raw data is well-aligned with recommender systems' needs for tackling…
Clique-width is a well-studied graph parameter. For graphs of bounded clique-width, many problems that are NP-hard in general can be polynomial-time solvable. The fact motivates several studies to investigate whether the clique-width of…
This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems.
We take an existing implementation of an algorithm for the maximum clique problem and modify it so that we can distribute it over an ad-hoc cluster of machines. Our goal was to achieve a significant speedup in performance with minimal…
We study two related problems concerning the number of homogeneous subsets of given size in graphs that go back to questions of Erd\H{o}s. Most notably, we improve the upper bounds on the Ramsey multiplicity of $K_4$ and $K_5$ and settle…
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…
In this paper, we study cliques and chromatic number of inhomogenous random graphs where the individual edge probabilities could be arbitrarily low. We use a recursive method to obtain estimates on the maximum clique size under a mild…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
A plank is the part of space between two parallel planes. The following open problem, posed 45 years ago, can be viwed as the converse of Tarski's plank problem (Bang's theorem): Is it true that if the total width of a collection of planks…
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinatorial designs which simultaneously provide a generalization…
We solve a question of Gowers from 2009 on clique differences in chains, thus ruling out any Sperner-type proof of the polynomial density Hales-Jewett theorem for alphabets of size 2.
We study graphs whose chromatic number is close to the order of the graph (the number of vertices). Both when the chromatic number is a constant multiple of the order and when the difference of the chromatic number and the order is a small…
Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best…
In this paper we give upper bounds on the number of minimal separators and potential maximal cliques of graphs w.r.t. two graph parameters, namely vertex cover ($\operatorname{vc}$) and modular width ($\operatorname{mw}$). We prove that for…
Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulations problems including Minimum Fill-in and Treewidth. We discover unexpected applications of…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…