The enumeration of permutations by inversions often leads to a q-analog of the usual generating 'nnetic,n. In this paper, two generalizations of the Worpitzky identity for the Eulerian numbers are obtained and used to enumerate permutations by the descent number and the major index of their inverses. The resulting (t, q)-generating series do in fact generalize the q-series obtainc? when countin...

The Generalized Pólya Urn (GPU) is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential estimation-adjusted urn model (a nonhomogeneous GPU) which has a wide spectrum of applications. Because the proposed urn model depends on sequential estimations of unknown...

We describe LMHS, an open source weighted partial maximum satisfiability (MaxSAT) solver. LMHS is a hybrid SAT-IP MaxSAT solver that implements the implicit hitting set approach to MaxSAT. On top of the main algorithm, LMHS offers integrated preprocessing, solution enumeration, an incremental API, and the use of a choice of SAT and IP solvers. We describe the main features of LMHS, and give emp...

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don't care sets. Speciically, given an incompletely speciied function g and a xed ordering of the variables, we propose an exact algorithm for selecting f such that f is a cover for g and the binary decision diagram for f is of minimum size. We proved that this problem is NP-complete. Here we show ...

This paper presents the results of experimentation on the development of an efficient branch-and-bound algorithm for the solution of zero-one linear mixed integer programming problems. An implicit enumeration is employed using bounds that are obtained from the fractional variables in the associated linear programming problem. The principal mathematical result used in obtaining these bounds is t...

In this report, we present our new worst-case execution time (WCET) analysis tool for Java processors, supporting both implicit path enumeration (IPET) and model checking based execution time estimation. Even though model checking is significantly more expensive than IPET, it offers new possibilities, such as modeling pipeline effects. Experimental results using UPPAAL indicate that model check...

We present geometric conditions that can be used to restrict or eliminate candidate topologes for Euclidean Steiner minimal trees in , d ≥ 2. Our emphasis is on conditions that are not restricted to the planar case (d = 2). For trees with a Steiner topology we give restrictions on terminal-Steiner connections that are based on the Voronoi diagram associated with the set of terminal nodes. We th...

Fulkerson et al. have given two examples of set covering problems that are empirically difficult to solve. They arise from Steiner triple systems and the larger problem, which has a constraint matrix of size 330 × 45 has only recently been solved. In this note, we show that the Steiner triple systems do indeed give rise to a series of problems that are probably hard to solve by implicit enumera...

A MULTI-STEP IMPLICIT ITERATIVE PROCESS FOR COMMON FIXED POINTS OF GENERALIZED C-OPERATORS IN CONVEX METRIC SPACES Zahid Akhtar, Hafiz Fukhar-ud-din, Ali Ahmad and Muhammad Ibrahim 1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan. College of computer Science and information systems, Jazan University, Jazan, Saudi Arabia. Center for Advanced Studies ...