相关论文: A polynomial-time randomized reduction from tourna…

It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…

It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We show that, analogously, the group isomorphism problem is…

Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…

We prove that isomorphism of tournaments of twin width at most $k$ can be decided in time $k^{O(\log k)}n^{O(1)}$. This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in…

In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…

An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…

Let $K$ be a full-dimensional convex subset of $\mathbb{R}^n$. We describe a new polynomial-time Turing reduction from the weak separation problem for $K$ to the weak optimization problem for $K$ that is based on a geometric heuristic. We…

We study two fundamental problems related to finding subgraphs: (1) given graphs G and H, Subgraph Test asks if H is isomorphic to a subgraph of G, (2) given graphs G, H, and an integer t, Packing asks if G contains t vertex-disjoint…

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…

Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…

The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…

We prove the unexpected result that almost uniform sampling of independent sets in graphs is possible via a probabilistic polynomial time algorithm. Note that our sampling algorithm (if correct) has extremely surprising consequences; the…

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…

Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…

Reid conjectured that any finite set of non-negative integers is the score set of some tournament and Yao gave a non-constructive proof of Reid's conjecture using arithmetic arguments. No constructive proof has been found since. In this…

In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…