In 1979, Valiant proved that computing the permanent of a 01-matrix is #PComplete. In this paper we present another proof for the same result. Our proof uses \black box" methodology, which facilitates its presentation. We also prove that deciding whether the permanent is divisible by a small prime is #P-Hard. We conclude by proving that a polynomially bounded function can not be #P-Complete und...

EEcient algorithm for model further extended to allow \dynamic membership" (to appear at INFOCOM'98). EEcient algorithm for low-degree multicast tree problem. 19 Conclusions Proposed algorithm produces near-optimal multicast trees for small and sparse networks. Quality of solution is maintained even when size and density of networks grow. Computation time is polynomially bounded and expected to...

We study multivariate integration of functions that are invariant under permutations (of subsets) of their arguments. We find an upper bound for the nth minimal worst case error and show that under certain conditions, it can be bounded independent of the number of dimensions. In particular, we study the application of unshifted and randomly shifted rank-1 lattice rules in such a problem setting...

The Cops and Robbers game as originally defined independently by Quilliot and by Nowakowski andWinkler in the 1980s has beenmuch studied, but very few results pertain to the algorithmic and complexity aspects of it. In this paper we prove that computing the minimumnumber of cops that are guaranteed to catch a robber on a given graph is NP-hard and that the parameterized version of the problem i...

We show that for a closed hyperbolic 3-manifold, the size of first eigenvalue Hodge Laplacian acting on coexact 1-forms is comparable to an isoperimetric ratio relating geodesic length and stable commutator with comparison constants depend polynomially volume lower bound injectivity radius, refining estimates Lipnowski Stern. use this estimate there exist sequences 3-manifolds radius bounded be...

It is shown that the discount factor needed to solve an undiscounted mean payoff stochastic game to optimality is exponentially close to 1, even in oneplayer games with a single random node and polynomially bounded rewards and transition probabilities. On the other hand, for the class of the so-called irreducible games with perfect information and a constant number of random nodes, we obtain a ...

The set system of all arithmetic progressions on [n] is known to have a discrepancy of order n1/4. We investigate the discrepancy for the set system S3 n formed by all sums of three arithmetic progressions on [n] and show that the discrepancy of S3 n is bounded below by Ω(n1/2). Thus S3 n is one of the few explicit examples of systems with polynomially many sets and a discrepancy this high.

In this article we study the hyperbolic problem (1) where R is a bounded region in Rn whose boundary is partitioned into disjoint sets ro, rl. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the ...

The famous 1960’s construction of Golod and Shafarevich yields infinite dimensional nil, but not nilpotent, algebras. However, these algebras have exponential growth. Here, we construct an infinite dimensional nil, but not nilporent, algebra which has polynomially bounded growth. 2000 Mathematics subject classification: 16N, 16P90. ∗Part of this work was done while the second author was visitin...

It is shown that the feasibly constructive arithmetic theory IPV does not prove (double negation of) LMIN(NP), unless the polynomial hierarchy CPV-provably collapses. It is proved that PV plus (double negation of) LMIN(NP) intuitionistically proves PIND(coNP). It is observed that PV+ PIND(NP∪coNP) does not intuitionistically prove NPB, a scheme which states that the extended Frege systems are n...