Mean-Cost cycles (MMCC). Experimental studies suggest that Howard’s algorithm works extremely well in this context. The theoretical complexity of Howard’s algorithm for finding MMCCs is a mystery. No polynomial time bound is known on its running time. Prior to this work, there were only linear lower

. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis. For the number of iterations of the MMCC algorithm we show an upper bound

We analyze the strong relationship among three combinatorial problems, namely the problem of sorting a permutation by the minimum number of reversals (MIN-SBR), the problem of finding the maximum number of edge-disjoint alternating cycles in a breakpoint graph associated with a given permutation

of the algorithm is O(N∆). We provide lower bounds on the minimum size of cycle-breaking sets for connected graphs. Further, we construct minimal cycle-breaking sets and establish bounds on the minimum fraction of prohibited turns for two important classes of graphs, namely, t-partite graphs and graphs with small

. This result is complemented by a lower bound of 48 n/8 ≥ 1.622 n. Then we present an algorithm which finds the minimum weight Hamilton cycle of a given 4-regular graph in time √ 3 n · poly(n) = O(1.733 n), improving a previous result of Eppstein. This algorithm can be modified to compute the number

This is a preliminary version of a Chapter on Algebraic Algorithms in the up-

characterization of the RKHS associated with the SLGM, we derive a lower bound on the minimum variance achievable by estimators with a prescribed bias function, including the important special case of unbiased estimation. This bound is obtained via an orthogonal projection of the prescribed mean function onto a

. This is the first strongly polynomial algorithm in over 35 years to improve upon some aspect of the O(nm) running time of the Bellman-Ford algorithm. The result extends to an O(n² log n) expected running time algorithm for finding the minimum mean cycle, an improvement over Karp's O(nm) worst-case time bound

quantified by isotopic non

cover with minimum weight. We particularly obtain a 2 3 approximation algorithm for the asymmetric maximum traveling salesman problem with distances zero and one and a 4 3 approximation algorithm for the asymmetric minimum traveling salesman problem with distances one and two. As a lower bound, we prove