In the Max Lin-2 problem we are given a system S of m linear equations in n variables over F2 in which Equation j is assigned a positive integral weight wj for each j. We wish to find an assignment of values to the variables which maximizes the total weight of satisfied equations. This problem generalizes Max Cut. The expected weight of satisfied equations is W/2, where W = w1 + · · ·+ wm; W/2 ...

Let S be a finite set with some rank function r such that the Whitney numbers w i = I { x e S I r ( x ) = i}l are log-concave. Given k, me N so that Wk-1 < Wk <~ Wk+m, set W = w k + w k + 1 + "'" + Wk + ~" Generalizing a theorem of Kleitman and Milner, we prove that every F ~ S with cardinality IFI/> Whas average rank at least ( k w k + ... + (k + m)wk+m)/W, provided the normalized profile vect...

Glushkov’s algorithm builds an ε-free nondeterministic automaton from a given regular expression. In the worst case, its number of states is linear and its number of transitions is quadratic in the size of the expression. We show in this paper that in average, the number of transitions is linear.

We prove a lower bound expressed in the increment sequence on the average-case complexity (number of inversions which is proportional to the running time) of Shellsort. This lower bound is sharp in every case where it could be checked. We obtain new results e.g. determining the average-case complexity precisely in the Yao-Janson-Knuth 3-pass case.

We prove a lower bound expressed in the increment sequence on the average-case complexity (number of inversions which is proportional to the running time) of Shellsort. This lower bound is sharp in every case where it could be checked. We obtain new results e.g. determining the average-case complexity precisely in the Yao-Janson-Knuth 3-pass case.

We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP, with a non-trivial success probability, for lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (i...

We introduce a new method for studying large scale properties of random walks. The new concepts of transience and recurrence on the average are compared with the ones introduced in [1] and with the usual ones; their relationships are analyzed and various examples are provided.

We present algorithms for sorting and routing on two-dimensional mesh-connected parallel architectures that are optimal on average. If one processor has many packets then we asymptotically halve the up to now best running times. For a load of one optimal algorithms are known for the mesh. We improve this to a load of eight without increasing the running time. For tori no optimal algorithms were...

The present talk summarizes the recently progressed state of a systematic re– evaluation of cosmological models that respect the presence of inhomogeneities. Emphasis is given to identifying the basic steps towards an effective (i.e. spatially averaged) description of structural evolution, also unfolding the various facets of a “smoothed–out” cosmology. We shall highlight some results obtained ...

An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimise the average time per transition and player Max wants to maximise it. A solution of averagetime games is presented using a reduction to average-price...