One popular and efficient scheme for solving combinatorial optimization problems over graphical models exactly is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This article 1) analyzes and demonstrates this inherent conflict between effective exploitation of problem decomposition (through AN...

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as (3, 3)hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite (3, 3)-hypergraphs. The proof tech...

let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...

‎the frobenius complement of a given frobenius group acts on its kernel‎. ‎the scheme which is arisen from the orbitals of this action is called ferrero pair scheme‎. ‎in this paper‎, ‎we show that the fibers of a ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality‎. ‎moreover‎, ‎it is shown that the restriction of a...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

We show that the topes of a complex oriented matroids (abbreviated COM) VC-dimension $d$ admit proper labeled sample compression scheme size $d$. This considerably extends results Moran and Warmuth authors is step towards conjecture -- one oldest open in computational learning theory. On hand, our approach exploits rich combinatorial cell structure COMs via matroid other hand viewing tope graph...

Let $p$ be a prime number and let $k$ an algebraically closed field of characteristic $p$. A $BT_1$ group scheme over is finite commutative which arises as the kernel on $p$-divisible (Barsotti–Tate) group. Our main result that every occurs direct factor $p$-torsion Jacobian explicit curve defined ${\mathbb F}_p$. We also treat variant with polarizations. tools are Kraft classification scheme...

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept introduce a Hamiltonian dynamics of the classical flux variables associated with quantum spins transverse-field Ising model. Molecular fluxes can be used as powerful preconditioner sort out frozen and ambivalent for annealers. performance accuracy our smooth ...