Lefteris M. Kirousis

On the algorithmic Lovász Local Lemma and acyclic edge coloring

The algorithm for Lovasz Local Lemma by Moser and Tardos gives a constructive way to prove the existence of combinatorial objects that satisfy a system of constraints. We present an alternative probabilistic analysis of the algorithm that does not involve reconstructing the history of the algorithm from the witness tree. We apply our technique to improve the best known upper bound to acyclic chromatic index. Specifically we show that a graph with maximum degree Δ has an acyclic proper edge coloring with at most ⌈3.74(Δ − 1)⌉ + 1 colors, whereas the previously known best bound was 4(Δ − 1). The same technique is also applied to improve corresponding bounds for graphs with bounded girth. An interesting aspect of this application is that the probability of the undesirable events do not have a uniform upper bound, i.e. it constitutes a case of the asymmetric Lovasz Local Lemma.

Acyclic edge coloring through the Lovász Local Lemma

We give a probabilistic analysis of a Moser-type algorithm for the Lov{a}sz Local Lemma (LLL), adjusted to search for acyclic edge colorings of a graph. We thus improve the best known upper bound to acyclic chromatic index, also obtained by analyzing a similar algorithm, but through the entropic method (basically counting argument). Specifically we show that a graph with maximum degree

Aggregation of Votes with Multiple Positions on Each Issue

Delta

An Alternate Proof of the Algorithmic Lovász Local Lemma

has an acyclic proper edge coloring with at most

On the Stability of Generalized Second Price Auctions with Budgets

lceil 3.74(Delta-1)rceil+1

On the Algorithmic Lov\'{a}sz Local Lemma

colors, whereas, previously, the best bound was

102.18 The problème des ménages revisited

4(Delta-1)

Alternative proofs of the asymmetric Lovász local lemma and Shearer's lemma

. The main contribution of this work is that it comprises a probabilistic analysis of a Moser-type algorithm applied to events pertaining to dependent variables.

On the Computational Complexity of Non-dictatorial Aggregation

We consider the problem of aggregating votes cast by a society on a fixed set of issues, where each member of the society may vote for one of several positions on each issue, but the combination of votes on the various issues is restricted to a set of feasible voting patterns. We require the aggregation to be supportive, i.e. for every issue

An interactive version of Lovász local lemma: Arthur and Merlin implement Moser's algorithm.

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