Among others, we show that every parameterized problem with a “linear OR” and with NP-hard underlying classical problem does not have a polynomial reduction to itself that assigns to every instance x with parameter k an instance y with |y| = k · |x|1−ε unless the polynomial hierarchy collapses to its third level (here ε is any given real number greater than zero).

Minimax Lower Bounds Adityanand Guntuboyina 2011 This thesis deals with lower bounds for the minimax risk in general decision-theoretic problems. Such bounds are useful for assessing the quality of decision rules. After providing a unified treatment of existing techniques, we prove new lower bounds which involve f -divergences, a general class of dissimilarity measures between probability measu...

We show lower bounds on the worst-case complexity of Shellsort. In particular, we give a fairly simple proof of an (n lg 2 n=(lg lg n) 2) lower bound for the size of Shellsort sorting networks, for arbitrary increment sequences. We also show an identical lower bound for the running time of Shellsort algorithms, again for arbitrary increment sequences. Our lower bounds establish an almost tight ...

We prove two statements. The rst one is a conjecture of Ian Hughes which states that if f1; : : : ; fn are primary invariants of a nite linear group G, then the least common multiple of the degrees of the fi is a multiple of the exponent of G. The second statement is about vector invariants: If G is a permutation group and K a eld of positive characteristic p such that p divides jGj, then the i...

The lower bounds on communication complexity measures of language generation by Parallel Communicating Grammar Systems (PCGS) are investigated. The rst result shows that there exists a language that can be generated by some dag-PCGS (PCGS with communication structures realizable by directed acyclic graphs) consisting of 3 grammars, but by no PCGS with tree communication structure. The second re...

Recently Fomin, Heggernes and Telle [Algorithmica 41 (2004) 73] introduced the notion of the treespan of a graph as a natural extension of the well-known bandwidth. They motivate this new concept from different viewpoints involving graph searching, tree decompositions and elimination orderings. In the present paper we prove several lower bounds on the treespan.  2005 Published by Elsevier B.V.

We derive lower bounds on the number of messages and the number of message delays required by a nonblocking fault-tolerant consensus algorithm, and we show that variants of the Paxos algorithm achieve those bounds.

We show that an oracle A that contains either 1/4 or 3/4 of all strings of length n can be used to separate EQP from the counting classes MODpkP, where p is a prime. Our proof makes use of the degree of a representing polynomial over Zpk . We show a linear lower bound on the degree of this polynomial. We also show an upper bound of O(n logp ) on the degree over the ring Zm, whenever m is a squa...

‎let $g$ be a finite group and $d_2(g)$ denotes the probability‎ ‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$‎. ‎we‎ ‎will obtain lower and upper bounds for $d_2(g)$ in the case where‎ ‎the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for‎ ‎all $xin g$‎. ‎also the given examples illustrate that all the‎ ‎bounds are sharp‎.

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.