Matching problems involve a set of participants, where each participant has a capacity and a subset of the participants rank a subset of the others in order of preference (strictly or with ties). Matching problems are motivated in practice by large-scale applications, such as automated matching schemes, which assign participants together based on their preferences over one another. This thesis ...

The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality...

The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality...

This paper presents a fast method for sparse decomposition of real second-order polynomial phase signals (PPSs). In the method, we first set three concatenate dictionaries to complete the sparse decomposition of real second-order polynomial phase signals. Three concatenate dictionaries are the frequency modulation dictionary, the frequency dictionary and the phase dictionary, respectively. Seco...

This paper deals with the stable b-matching problem on general multigraphs. We generalize the notion of singular and dual rotation and establish a one-one correspondence between stable b-matchings and certain sets of rotations. This correspondence is used to find all stable edges and a minimum regret stable b-matching in polynomial time. We also recall the NP-completeness of the egalitarian sta...

We show that the class FBV of [0, 1]-valued functions with total variation at most 1 can be agnostically learned with respect to the absolute loss in polynomial time from O ( 1 2 log 1 δ ) examples, matching a known lower bound to within a constant factor. We establish a bound of O(1/m) on the expected error of a polynomial-time algorithm for learning FBV in the prediction model, also matching ...

We study a natural generalization of stable matching to the maximumweight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG. We give the first polynomial time algorithm for the latter problem; this algorithm is also combinatorial. The combinatorial nature of our algorithms not only ...

A simple 2-matching in a graph is a subgraph all of whose nodes have degree 1 or 2. A simple 2-matching is called k-restricted if every connected component has > k edges. We consider the problem of finding a k-restricted simple 2-matching with a maximum number of edges, which is a relaxation of the problem of finding a Hamilton cycle in a graph. Our main result is a min-max theorem for the maxi...

For an undirected graph and a fixed integer k, a 2-matching is said to be Ck-free if it has no cycle of length k or less. In particular, a C4-free 2-matching in a bipartite graph is called a square-free 2-matching. The problem of finding a maximum Ck-free 2-matching in a bipartite graph is NP-hard when k ≥ 6, and polynomially solvable when k = 4. Also, the problem of finding a maximum-weight Ck...

2-dimensional Matching Problem, which requires to find a matching of leftto rightvertices in a balanced 2n-vertex bipartite graph, is a well-known polynomial problem, while various variants, like the 3-dimensional analogoue (3DM, with triangles on a tripartite graph), or the Hamiltonian Circuit Problem (HC, a restriction to “unicyclic” matchings) are among the main examples of NP-hard problems,...