Results 1  10
of
14
Geometry of neighborjoining algorithm for small trees
 PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON ALGEBRAIC BIOLOGY
, 2008
"... In 2007, Eickmeyer et al. showed that the tree topologies outputted by the NeighborJoining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps R (n2) , where n is the numbe ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
In 2007, Eickmeyer et al. showed that the tree topologies outputted by the NeighborJoining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps R (n2) , where n
Satisfiability Allows No Nontrivial Sparsification Unless The PolynomialTime Hierarchy Collapses
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 38 (2010)
, 2010
"... Consider the following twoplayer communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small ..."
Abstract

Cited by 53 (2 self)
 Add to MetaCart
Consider the following twoplayer communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small cost, where the cost measure is the number of bits of communication from the first player to the second player. For any integer d ≥ 3 and positive real ǫ we show that if satisfiability for nvariable dCNF formulas has a protocol of cost O(n d−ǫ) then coNP is in NP/poly, which implies that the polynomialtime hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for ǫ = 0. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several areas, namely sparsification, kernelization in parameterized complexity, lossy compression, and probabilistically checkable proofs. By reduction, similar results hold for other NPcomplete problems. For the vertex cover problem on nvertex duniform hypergraphs, the above statement holds for any integer d ≥ 2. The case d = 2 implies that no NPhard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of O(k 2−ǫ) edges unless coNP is in NP/poly, where k denotes the size of the deletion set. Kernels consisting of O(k 2) edges are known for several problems in the class, including vertex cover, feedback vertex set, and boundeddegree deletion.
NonDefinability Results for Randomised FirstOrder Logic
"... We investigate the expressive power of randomised firstorder logic (BPFO) on restricted classes of structures. While BPFO is stronger than FO in general, even on structures with a builtin addition relation, we show that BPFO is not stronger than FO on structures with a unary vocabulary, nor on the ..."
Abstract
 Add to MetaCart
We investigate the expressive power of randomised firstorder logic (BPFO) on restricted classes of structures. While BPFO is stronger than FO in general, even on structures with a builtin addition relation, we show that BPFO is not stronger than FO on structures with a unary vocabulary, nor on the class of equivalence relations. The same techniques can be applied to show that evenness of a linear order, and therefore graph connectivity, can not be defined in BPFO. Finally, we show that there is an FO[≤]definable query on word structures which can not be defined in BPFO[+1].
Algorithms for Molecular Biology Open AccessResearch On the optimality of the neighborjoining algorithm
, 2008
"... On the optimality of the neighborjoining algorithm ..."
Partitioning the Sample Space on Five Taxa for the Neighbor Joining Algorithm
, 2007
"... In this paper, we will analyze the behavior of the Neighbor Joining algorithm on five taxa and we will show that the partition of the sample (data) space for estimation of a tree topology with five taxa into subspaces, within each of which the Neighbor Joining algorithm returns the same tree topolog ..."
Abstract
 Add to MetaCart
In this paper, we will analyze the behavior of the Neighbor Joining algorithm on five taxa and we will show that the partition of the sample (data) space for estimation of a tree topology with five taxa into subspaces, within each of which the Neighbor Joining algorithm returns the same tree topology. A key of our method to partition the sample space is the action of the symmetric group S5 on the set of distance matrices by changing the labels of leaves. The method described in this paper can be generalized to trees with more than five taxa.
Randomness buys depth for approximate counting
, 2010
"... We show that the promise problem of distinguishing nbit strings of hamming weight ≥ 1/2 + Ω(1 / lg d−1 n) from strings of weight ≤ 1/2 − Ω(1 / lg d−1 n) can be solved by explicit, randomized (unboundedfanin) poly(n)size depthd circuits with error ≤ 1/3, but cannot be solved by deterministic pol ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
We show that the promise problem of distinguishing nbit strings of hamming weight ≥ 1/2 + Ω(1 / lg d−1 n) from strings of weight ≤ 1/2 − Ω(1 / lg d−1 n) can be solved by explicit, randomized (unboundedfanin) poly(n)size depthd circuits with error ≤ 1/3, but cannot be solved by deterministic poly(n)size depth(d+1) circuits, for every d ≥ 2. This matches the simulation of the first type of circuits by the latter type of circuits with depth d+2 by Ajtai (Ann. Pure Appl. Logic; ’83), and provides an example where randomization (provably) buys resources. Techniques: To rule out deterministic circuits we combine the switching lemma with an earlier depth3 lower bound by the author (Comp. Complexity 2009). To exhibit randomized circuits we combine recent analyses by Amano (ICALP ’09) and Brody and Verbin (FOCS ’10) with derandomization. To make these circuits explicit – which we find important for the main message of this paper – we construct a new pseudorandom generator for certain combinatorial rectangle tests. Based on expander walks, the generator for example fools tests A1 ×A2 ×...×Alg n for Ai ⊆ [n], Ai  = n/2 with error 1/n and seed length O(lg n), improving on previous constructions for this basic setting. Supported by NSF grant CCF0845003.
defined processes in L p
"... In this paper we derive a limit theorem for recursively defined processes. For several instances of recursive processes like for depth first search processes in random trees with logarithmic height or for fractal processes it turns out that convergence can not be expected in the space of continuous ..."
Abstract
 Add to MetaCart
In this paper we derive a limit theorem for recursively defined processes. For several instances of recursive processes like for depth first search processes in random trees with logarithmic height or for fractal processes it turns out that convergence can not be expected in the space of continuous functions or in the Skorohod space D. We therefore weaken the Skorohod topology and establish a convergence result in L p spaces in which D is continuously imbedded. The proof of our convergence result is based on an extension of the contraction method. An application of the limit theorem is given to the FIND process. The paper extends in particular results in [HR00] on the existence and uniqueness of random fractal measures and processes. The depth first search processes of Catalan and of logarithmically growing trees do however not fit the assumptions of our limit theorem and lead to the so far unsolved problem of degenerate limits.
Approximation of Natural W[P]complete Minimisation Problems is Hard
"... We prove that the weighted monotone circuit satisfiability problem has no fixedparameter tractable approximation algorithm with constant or polylogarithmic approximation ratio unless FPT = W[P]. Our result answers a question of Alekhnovich and Razborov [2], who proved that the weighted monotone cir ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We prove that the weighted monotone circuit satisfiability problem has no fixedparameter tractable approximation algorithm with constant or polylogarithmic approximation ratio unless FPT = W[P]. Our result answers a question of Alekhnovich and Razborov [2], who proved that the weighted monotone circuit satisfiability problem has no fixedparameter tractable 2approximation algorithm unless every problem in W[P] can be solved by a randomized fpt algorithm and asked whether their result can be derandomized. Alekhnovich and Razborov used their inapproximability result as a lemma for proving that resolution is not automatizable unless W[P] is contained in randomized FPT. It is an immediate consequence of our result that the complexity theoretic assumption can be weakened to W[P] ̸ = FPT. The decision version of the monotone circuit satisfiability problem is known to be complete for the class W[P]. By reducing them to the monotone circuit satisfiability problem with suitable approximation preserving reductions, we prove similar inapproximability results for all other natural minimisation problems known to be W[P]complete.
RANDOMISATION AND DERANDOMISATION IN DESCRIPTIVE COMPLEXITY THEORY
, 2010
"... Vol. 7 (3:14) 2011, pp. 1–24 ..."
Results 1  10
of
14