The {\it nucleon} is introduced as a new allocation concept for
non-negative cooperative n-person transferable utility games.
The nucleon may be viewed as the multiplicative analogue of
Schmeidler's nucleolus.
It is shown that the nucleon of (not necessarily bipartite) matching
games ... more >>>

We show that the perfect matching problem is in the
complexity class SPL (in the nonuniform setting).
This provides a better upper bound on the complexity of the
matching problem, as well as providing motivation for studying
the complexity class SPL.

Using similar ... more >>>

We study bounded degree graph problems, mainly the problem of
k-Dimensional Matching \emph{(k-DM)}, namely, the problem of
finding a maximal matching in a k-partite k-uniform balanced
hyper-graph. We prove that k-DM cannot be efficiently approximated
to within a factor of $ O(\frac{k}{ \ln k}) $ unless $P = NP$.
This ... more >>>

We study small degree graph problems such as Maximum Independent Set
and Minimum Node Cover and improve approximation lower bounds for
them and for a number of related problems, like Max-B-Set Packing,
Min-B-Set Cover, Max-Matching in B-uniform 2-regular hypergraphs.
For example, we prove NP-hardness factor of 95/94
more >>>

We study computational problems that arise in the context of iterated dominance in anonymous games, and show that deciding whether a game can be solved by means of iterated weak dominance is NP-hard for anonymous games with three actions. For the case of two actions, this problem can be reformulated ... more >>>

The problem of finding a nontrivial factor of a polynomial $f(x)$ over a finite field $\mathbb{F}_q$ has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the generalized Riemann hypothesis (GRH). In this work we improve the state of the ... more >>>

The resolution complexity of the perfect matching principle was studied by Razborov [Raz04], who developed a technique for proving its lower bounds for dense graphs. We construct a constant degree bipartite graph $G_n$ such that the resolution complexity of the perfect matching principle for $G_n$ is $2^{\Omega(n)}$, where $n$ is ... more >>>

Recently, perfect matching in bounded planar cutwidth bipartite graphs
$BGGM$ was shown to be in ACC$^0$ by Hansen et al.. They also conjectured that
the problem is in AC$^0$.
In this paper, we disprove their conjecture by showing that the problem is
not in AC$^0[p^{\alpha}]$ for every prime $p$. ... more >>>

We show that given an embedding of an O(log n) genus bipartite graph, one can construct an edge weight function in logarithmic space, with respect to which the minimum weight perfect matching in the graph is unique, if one exists.

As a consequence, we obtain that deciding whether the ... more >>>