We study the space X (G) of pictures of a graph G in complex projective d-space. The main result is that the homology groups (with integer coefficients) of X (G) are completely determined by the Tutte polynomial of G. One application is a criterion in terms of the Tutte polynomial for independence in the d-parallel matroids studied in combinatorial rigidity theory. For certain special graphs ca...

Many problems in data mining can be viewed as a special case of the problem of enumerating the closed elements of an independence system with respect to some specific closure operator. Motivated by real-world applications, e.g., in track mining, we consider a generalization of this problem to strongly accessible set systems and arbitrary closure operators. For this more general problem setting,...

The robustness function of a matroid measures the maximum increase in the weight of its minimum weight bases that can be produced by increases of a given total cost on the weights of its elements. We present an algorithm for computing this function, that runs in strongly polynomial time for matroids in which independence can be tested in strongly polynomial time. We identify key properties of t...

Let G be a multigraph. We study the space X (G) of all pictures of G in complex projective d-space. The main result is that the homology groups (with integer coefficients) of X (G) are completely determined by the Tutte polynomial of G. One application is a criterion in terms of the Tutte polynomial for independence in the d-parallel matroids studied in combinatorial rigidity theory. In the cas...

In this paper we first propose two new concepts concerning the notion of key escrow schemes: provable partiality and independence. Roughly speaking, a scheme has provable partiality if the existence of a polynomial time for recovering the secret from escrowed information implies there is a polynomial time algorithm for solving a well known intractable problem. A scheme is independent if the sec...

We study the growth rate on the number obstructions (forbidden minors) for families of graphs that are based on parameterized graph problems. Our main result shows that if the de ning graph problem is NP-complete then the growth rate on the number of obstructions must be super-polynomial or else the polynomial-time hierarchy must collapse to P 3 . We illustrate the rapid growth rate of paramete...

This paper proposes a method for blind system identification based on the independence of input signals. Under the assumption that the system is MIMO, square, and represented by a polynomial matrix fraction with constant numerator matrix, the method makes it possible to identify the system without observation of input signals. This rather challenging problem is solved by applying independent co...

Action-Graph Games (AGGs) (Bhat & Leyton-Brown 2004) are a fully expressive game representation which can compactly express strict and context-specific independence and anonymity structure in players’ utility functions. We present an efficient algorithm for computing expected payoffs under mixed strategy profiles. This algorithm runs in time polynomial in the size of the AGG representation (whi...

Abstract Explicit expressions for restricted partition function W (s, d) and its quasiperiodic components W j (s, dm) (called Sylvester waves) for a set of positive integers dm = {d1, d2, . . . , dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli and Eulerian polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester ...

A matroid on a set E is a family I of subsets of E (called independent sets) with the properties • a subset of an independent set is independent; • if A and B are independent with |A| < |B|, then there exists x ∈ B \A such that A∪{x} is independent. The rank ρ(A) of a subset A of E is the common size of maximal independent subsets of A. Examples of matroids: • E is a family of vectors in a vect...