Codeword stabilized quantum codes: algorithm and structure

The codeword stabilized ("CWS") quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021). This formalism reduces the problem of constructing such quantum codes to finding a binary classical code correcting an error pattern induced by a graph state. Finding such a classical code can be very difficult. Here, we consider an algorithm which maps the search for CWS codes to a problem of identifying maximum cliques in a graph. While solving this problem is in general very hard, we prove three structure theorems which reduce the search space, specifying certain admissible and optimal ((n,K,d)) additive codes. In particular, we find there does not exist any ((7,3,3)) CWS code though the linear programming bound does not rule it out. The complexity of the CWS search algorithm is compared with the contrasting method introduced by Aggarwal and Calderbank (arXiv:cs/0610159).Comment: 11 pages, 1 figur

Construction of near-optimal vertex clique covering for real-world networks

We propose a method based on combining a constructive and a bounding heuristic to solve the vertex clique covering problem (CCP), where the aim is to partition the vertices of a graph into the smallest number of classes, which induce cliques. Searching for the solution to CCP is highly motivated by analysis of social and other real-world networks, applications in graph mining, as well as by the fact that CCP is one of the classical NP-hard problems. Combining the construction and the bounding heuristic helped us not only to find high-quality clique coverings but also to determine that in the domain of real-world networks, many of the obtained solutions are optimal, while the rest of them are near-optimal. In addition, the method has a polynomial time complexity and shows much promise for its practical use. Experimental results are presented for a fairly representative benchmark of real-world data. Our test graphs include extracts of web-based social networks, including some very large ones, several well-known graphs from network science, as well as coappearance networks of literary works' characters from the DIMACS graph coloring benchmark. We also present results for synthetic pseudorandom graphs structured according to the Erdös-Renyi model and Leighton's model

Activity recognition from videos with parallel hypergraph matching on GPUs

In this paper, we propose a method for activity recognition from videos based on sparse local features and hypergraph matching. We benefit from special properties of the temporal domain in the data to derive a sequential and fast graph matching algorithm for GPUs. Traditionally, graphs and hypergraphs are frequently used to recognize complex and often non-rigid patterns in computer vision, either through graph matching or point-set matching with graphs. Most formulations resort to the minimization of a difficult discrete energy function mixing geometric or structural terms with data attached terms involving appearance features. Traditional methods solve this minimization problem approximately, for instance with spectral techniques. In this work, instead of solving the problem approximatively, the exact solution for the optimal assignment is calculated in parallel on GPUs. The graphical structure is simplified and regularized, which allows to derive an efficient recursive minimization algorithm. The algorithm distributes subproblems over the calculation units of a GPU, which solves them in parallel, allowing the system to run faster than real-time on medium-end GPUs

A novel evolutionary formulation of the maximum independent set problem

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs