Graph Searching, Parity Games and Imperfect Information

We investigate the interrelation between graph searching games and games with imperfect information. As key consequence we obtain that parity games with bounded imperfect information can be solved in PTIME on graphs of bounded DAG-width which generalizes several results for parity games on graphs of bounded complexity. We use a new concept of graph searching where several cops try to catch multiple robbers instead of just a single robber. The main technical result is that the number of cops needed to catch r robbers monotonously is at most r times the DAG-width of the graph. We also explore aspects of this new concept as a refinement of directed path-width which accentuates its connection to the concept of imperfect information

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

LOW-COMPLEXITY AND HIGH-PERFORMANCE SOFT MIMO DETECTION BASED ON DISTRIBUTED M-ALGORITHM THROUGH TRELLIS-DIAGRAM

This paper presents a novel low-complexity multiple-input multipleoutput (MIMO) detection scheme using a distributed M-algorithm (DM) to achieve high performance soft MIMO detection. To reduce the searching complexity, we build a MIMO trellis graph and split the searching operations among different nodes, where each node will apply the M-algorithm. Instead of keeping a global candidate list as the traditional detector does, this algorithm keeps multiple small candidate lists to generate soft information. Since the DM algorithm can achieve good BER performance with a small M, the sorting cost of the DM algorithm is lower than that of the conventional K-best MIMO algorithm. The proposed algorithm is very suitable for high speed parallel processing.NokiaNokia Siemens Networks (NSN)XilinxNational Science Foundatio

Exclusive graph searching vs. pathwidth

International audienceIn Graph Searching, a team of searchers aims at capturing an invisible fugitive moving arbitrarily fast in a graph. Equivalently, the searchers try to clear a contaminated network. The problem is to compute the minimum number of searchers required to accomplish this task. Several variants of Graph Searching have been studied mainly because of their close relationship with the pathwidth of a graph. Blin et al. defined the Exclusive Graph Searching where searchers cannot " jump " and no node can be occupied by more than one searcher. In this paper, we study the complexity of this new variant. We show that the problem is NP-hard in planar graphs with maximum degree 3 and it can be solved in linear-time in the class of cographs. We also show that monotone Exclusive Graph Searching is NP-complete in split graphs where Pathwidth is known to be solvable in polynomial time. Moreover, we prove that monotone Exclusive Graph Searching is in P in a subclass of star-like graphs where Pathwidth is known to be NP-hard. Hence, the computational complexities of monotone Exclusive Graph Searching and Pathwidth cannot be compared. This is the first variant of Graph Searching for which such a difference is proved

An efficient least common subgraph algorithm for video indexing

Many tasks in computer vision can be expressed as graph problems. This allows the task to be solved using a well studied algorithm, however many of these algorithms are of exponential complexity. This is a disadvantage when considered in the context of searching a database of images or videos for similarity. Work by Mesaner and Bunke (1995) has suggested a new class of graph matching algorithms which uses a priori knowledge about a database of models to reduce the time taken during online classification. This paper presents a new algorithm which extends the earlier work to detection of the largest common subgraph.<br /