Worst-Case Vs. Algorithmic Average-Case Complexity in the Polynomial-Time Hierarchy

2006 ◽  
pp. 386-397 ◽  
Author(s):  
Dan Gutfreund
Keyword(s):  
Polynomial Time ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Polynomial Time Hierarchy

scholarly journals TIME OPTIMAL ALGORITHMS FOR BLACK HOLE SEARCH IN RINGS

2011 ◽  
Vol 03 (04) ◽  
pp. 457-471 ◽  
Author(s):  
B. BALAMOHAN ◽  
P. FLOCCHINI ◽  
A. MIRI ◽  
N. SANTORO
Keyword(s):  
Black Hole ◽  
Time Complexity ◽  
Time Cost ◽  
Ring Networks ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Time Optimal ◽  
Optimal Average

In a network environment supporting mobile entities (called robots or agents), a black hole is a harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problit is the task of a team of k > 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this paper, we consider the black hole search problit in asynchronous ring networks of n nodes, and focus on time complexity. It is known that any algorithm for black-hole search in a ring requires at least 2(n - 2) time in the worst case. The best known algorithm achieves this bound with a team of n - 1 agents with an average time cost of 2(n - 2), equal to the worst case. In this paper, we first show how the same number of agents using 2 extra time units in the worst case, can solve the problit in only [Formula: see text] time on the average. We then prove that the optimal average case complexity of [Formula: see text] can be achieved without increasing the worst case using 2(n - 1) agents. Finally, we design an algorithm that achieves asymptotically optimal both worst and average case time complexities itploying an optimal team of k = 2 agents, thus improving on the earlier results that required O(n) agents.

scholarly journals Asymptotic and Exact Results on the Complexity of the Novelli-Pak-Stoyanovskii Algorithm

10.37236/6354 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Carsten Schneider ◽  
Robin Sulzgruber
Keyword(s):  
Exact Formula ◽  
Sorting Algorithm ◽  
Limit Curve ◽  
Hook Length ◽  
Asymptotic Results ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Worst Case Complexity

The Novelli-Pak-Stoyanovskii algorithm is a sorting algorithm for Young tableaux of a fixed shape that was originally devised to give a bijective proof of the hook-length formula. We obtain new asymptotic results on the average case and worst case complexity of this algorithm as the underlying shape tends to a fixed limit curve. Furthermore, using the summation package Sigma we prove an exact formula for the average case complexity when the underlying shape consists of only two rows. We thereby answer questions posed by Krattenthaler and Müller.

scholarly journals Junta Distributions and the Average-Case Complexity of Manipulating Elections

2007 ◽  
Vol 28 ◽  
pp. 157-181 ◽  
Author(s):  
A. D. Procaccia ◽  
J. S. Rosenschein
Keyword(s):  
Computational Complexity ◽  
Strategic Behavior ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
New Concepts ◽  
Np Hardness

Encouraging voters to truthfully reveal their preferences in an election has long been an important issue. Recently, computational complexity has been suggested as a means of precluding strategic behavior. Previous studies have shown that some voting protocols are hard to manipulate, but used NP-hardness as the complexity measure. Such a worst-case analysis may be an insufficient guarantee of resistance to manipulation. Indeed, we demonstrate that NP-hard manipulations may be tractable in the average case. For this purpose, we augment the existing theory of average-case complexity with some new concepts. In particular, we consider elections distributed with respect to junta distributions, which concentrate on hard instances. We use our techniques to prove that scoring protocols are susceptible to manipulation by coalitions, when the number of candidates is constant.

Worst-case versus average case complexity of ray-shooting

Computing ◽  
1998 ◽  
Vol 61 (2) ◽  
pp. 103-131 ◽  
Author(s):  
L. Szirmay-Kalos ◽  
G. Márton
Keyword(s):  
Worst Case ◽  
Average Case ◽  
Ray Shooting ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Case Versus

On quantum one-way permutations

2002 ◽  
Vol 2 (5) ◽  
pp. 379-398
Author(s):  
E. Kashefi ◽  
H. Nishimura ◽  
V. Vedral
Keyword(s):  
Quantum States ◽  
Grover’S Algorithm ◽  
Worst Case ◽  
Quantum Networks ◽  
Average Case ◽  
Case Complexity ◽  
Polynomial Size ◽  
Average Case Complexity ◽  
Grover's Algorithm ◽  
The Relationship

\We discuss the question of the existence of quantum one-way permutations. First, we consider the question: if a state is difficult to prepare, is the reflection operator about that state difficult to construct? By revisiting Grover's algorithm, we present the relationship between this question and the existence of quantum one-way permutations. Next, we prove the equivalence between inverting a permutation and that of constructing polynomial size quantum networks for reflection operators about a class of quantum states. We will consider both the worst case and the average case complexity scenarios for this problem. Moreover, we compare our method to Grover's algorithm and discuss possible applications of our results.

Guest Column

2021 ◽  
Vol 52 (1) ◽  
pp. 47-69
Author(s):  
R. Pass ◽  
M. Venkitasubramaniam
Keyword(s):  
Recent Result ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Average Case ◽  
Interactive Games ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Probabilistic Polynomial Time

We review a study of average-case complexity through the lens of interactive puzzles- interactive games between a computationally bounded Challenger and computationally-bounded Solver/Attacker. Most notably, we use this treatment to review a recent result showing that if NP is hard-on-the-average, then there exists a sampleable distribution over only true statements of an NP language, for which no probabilistic polynomial time algorithm can find witnesses. We also discuss connections to the problem of whether average-case hardness in NP implies averagecase hardness in TFNP, or the existence of cryptographic one-way functions.

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