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We present exact calculations of reliability polynomials R(G, p) for lattice stripsG of fixed widths Ly ≤ 4 and arbitrarily great length Lx with various boundary conditions. We introduce the notion of a reliability per vertex, r({G}, p) = lim|V |→∞R(G, p)1/|V | where |V | denotes the number of vertices in G and {G} denotes the formal limit lim|V |→∞G. We(More)
Many problems in resource allocations, memory allocation, and distributed computer system design can be formulated as problems of packing variablesized items into fixed-sized containers in order to minimize the total number of containers used. In this paper, a generalized packing algorithm that encompasses many well-known heuristic packing algorithms is(More)
The change-making problem (assemble a to ta l of C cents using the least number of coins) is r epresen ta t ive of a f requent ly encountered class of opt imizat ion problems. A recursive a lgor i thm is developed for solving t h a t problem. A much s imp le r -bu t not universal ly appl icable-a lgor i thm is also presented, and a procedure is described(More)
We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex square-lattice strip graphs G for a variety of transverse widths Lt and for arbitrarily great length Ll, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the(More)
We present exact calculations of the partition function of the q-state Potts model for general q and temperature on strips of the square lattice of width Ly = 3 vertices and arbitrary length Lx with periodic longitudinal boundary conditions, of the following types: (i) (FBCy , PBCx) = cyclic, (ii) (FBCy, TPBCx) = Möbius, (iii) (PBCy , PBCx) = toroidal, and(More)
We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic(More)
In this paper we present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex strip graphs, of width Ly = 2 and arbitrary length, of the triangular lattice with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to(More)
We present exact calculations of the partition function of the q-state Potts model on (i) open, (ii) cyclic, and (iii) Möbius strips of the honeycomb (brick) lattice of width Ly = 2 and arbitrarily great length. In the infinite-length limit the thermodynamic properties are discussed. The continuous locus of singularities of the free energy is determined in(More)