Efficient Enumeration of Bipartite Subgraphs in Graphs

Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many efficient enumeration algorithms for the fundamental substructures such as spanning trees, cycles, and paths, have been developed. This paper addresses the enumeration problem of bipartite subgraphs. Even though bipartite graphs are quite fundamental and have numerous applications in both theory and application, its enumeration algorithms have not been intensively studied, to the best of our knowledge. We propose the first non-trivial algorithms for enumerating all bipartite subgraphs in a given graph. As the main results, we develop two efficient algorithms: the one enumerates all bipartite induced subgraphs of a graph with degeneracy $k$ in $O(k)$ time per solution. The other enumerates all bipartite subgraphs in $O(1)$ time per solution

New Computational Upper Bounds for Ramsey Numbers R(3,k)

Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numbers: R(3,10) <= 42, R(3,11) <= 50, R(3,13) <= 68, R(3,14) <= 77, R(3,15) <= 87, and R(3,16) <= 98. All of them are improvements by one over the previously best known bounds. Let e(3,k,n) denote the minimum number of edges in any triangle-free graph on n vertices without independent sets of order k. The new upper bounds on R(3,k) are obtained by completing the computation of the exact values of e(3,k,n) for all n with k <= 9 and for all n <= 33 for k = 10, and by establishing new lower bounds on e(3,k,n) for most of the open cases for 10 <= k <= 15. The enumeration of all graphs witnessing the values of e(3,k,n) is completed for all cases with k <= 9. We prove that the known critical graph for R(3,9) on 35 vertices is unique up to isomorphism. For the case of R(3,10), first we establish that R(3,10) = 43 if and only if e(3,10,42) = 189, or equivalently, that if R(3,10) = 43 then every critical graph is regular of degree 9. Then, using computations, we disprove the existence of the latter, and thus show that R(3,10) <= 42.Comment: 28 pages (includes a lot of tables); added improved lower bound for R(3,11); added some note

COMPARISON OF TWO NOVEL LIST SPHERE DETECTOR ALGORITHMS FOR MIMO-OFDM SYSTEMS

In this paper, the complexity and performance of two novel list sphere detector (LSD) algorithms are studied and evaluated in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system. The LSDs are based on the K-best and the Schnorr-Euchner enumeration (SEE) algorithms. The required list sizes for LSD algorithms are determined for a 2×2 system with 4- quadrature amplitude modulation (QAM), 16-QAM, and 64-QAM. The complexity of the algorithms is compared by studying the number of visited nodes per received symbol vector by the algorithm in computer simulations. The SEE based LSD algorithm is found to be a less complex and a feasible choice for implementation compared to the K-best based LSD algorithm.ElekrobitNokiaTexas InstrumentsFinnish Funding Agency for Technology and InnovationTeke