Related papers: Heuristic algorithm for solving of the graph isomo…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
The graph isomorphism problem remains a fundamental challenge in computer science, driving the search for efficient decision algorithms. Due to its ambiguous computational complexity, heuristic approaches such as simulated annealing are…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject…
We consider the isomorphism problem for hypergraphs taking as input two hypergraphs over the same set of vertices $V$ and a permutation group $\Gamma$ over domain $V$, and asking whether there is a permutation $\gamma \in \Gamma$ that…
We investigate classical and quantum physics-based algorithms for solving the graph isomorphism problem. Our work integrates and extends previous work by Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et al.…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the ob- servation of smaller graphs and basic structure of our heuristics.…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…
The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is…
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…
Twin-width is a graph parameter introduced in the context of first-order model checking, and has since become a central parameter in algorithmic graph theory. While many algorithmic problems become easier on arbitrary classes of bounded…
We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this…
We address the inverse Frobenius--Perron problem: given a prescribed target distribution $\rho$, find a deterministic map $M$ such that iterations of $M$ tend to $\rho$ in distribution. We show that all solutions may be written in terms of…
In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…