Different Speeds Suffice for Rendezvous of Two Agents on Arbitrary Graphs

2017 ◽  
pp. 79-90 ◽  
Author(s):  
Evangelos Kranakis ◽  
Danny Krizanc ◽  
Euripides Markou ◽  
Aris Pagourtzis ◽  
Felipe Ramírez
Keyword(s):  
Two Agents ◽  
Arbitrary Graphs

scholarly journals Improving the Smoothed Complexity of FLIP for Max Cut Problems

2021 ◽  
Vol 17 (3) ◽  
pp. 1-38
Author(s):  
Ali Bibak ◽  
Charles Carlson ◽  
Karthekeyan Chandrasekaran
Keyword(s):  
General Framework ◽  
Edge Weight ◽  
Complete Graphs ◽  
Worst Case ◽  
Weight Density ◽  
Complete Problems ◽  
Substantial Progress ◽  
Run Time ◽  
Optimum Solution ◽  
Arbitrary Graphs

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .

scholarly journals Truthful fair division without free disposal

2020 ◽  
Vol 55 (3) ◽  
pp. 523-545 ◽  
Author(s):  
Xiaohui Bei ◽  
Guangda Huzhang ◽  
Warut Suksompong
Keyword(s):  
Fair Division ◽  
Multiple Agents ◽  
Two Agents ◽  
Free Disposal ◽  
Cake Cutting ◽  
Strategic Agents ◽  
Additional Constraints

Abstract We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

scholarly journals A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

2019 ◽  
Vol 22 (5) ◽  
pp. 837-844
Author(s):  
Gareth Wilkes
Keyword(s):  
Fundamental Group ◽  
Infinite Graphs ◽  
Graphs Of Groups ◽  
Arbitrary Graphs

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.

Rationality and Strongly Polynomial Solvability of Eisenberg–Gale Markets with Two Agents

2010 ◽  
Vol 24 (3) ◽  
pp. 1117-1136 ◽  
Author(s):  
Deeparnab Chakrabarty ◽  
Nikhil R. Devanur ◽  
Vijay V. Vazirani
Keyword(s):  
Polynomial Solvability ◽  
Two Agents ◽  
Strongly Polynomial

scholarly journals Development of a Two-Step Route to 3-PBC and βCCt, Two Agents Active against Alcohol Self-Administration in Rodent and Primate Models

2011 ◽  
Vol 76 (11) ◽  
pp. 4721-4727 ◽  
Author(s):  
Ojas A. Namjoshi ◽  
Angelica Gryboski ◽  
German O. Fonseca ◽  
Michael L. Van Linn ◽  
Zhi-jian Wang ◽  
...  
Keyword(s):  
Self Administration ◽  
Two Agents

TWO AGENTS FOR ANAESTHESIA INDUCTION

InPharma ◽  
1976 ◽  
Vol 53 (1) ◽  
pp. 9-9
Keyword(s):  
Anaesthesia Induction ◽  
Two Agents

scholarly journals Succinct encoding of arbitrary graphs

2013 ◽  
Vol 513 ◽  
pp. 38-52 ◽  
Author(s):  
Arash Farzan ◽  
J. Ian Munro
Keyword(s):  
Arbitrary Graphs

A Comparison of Transmitter and Synephrine on Luminescence Induction in the Firefly Larva

1972 ◽  
Vol 57 (3) ◽  
pp. 737-743
Author(s):  
ALBERT D. CARLSON
Keyword(s):  
Monoamine Oxidase ◽  
Extinction Rate ◽  
Pharmacological Effects ◽  
Response Latencies ◽  
Atp Production ◽  
Two Agents ◽  
Oxidase Enzyme ◽  
The Difference

1. The pharmacological effects of neural transmitter and synephrine are compared with respect to induction of luminescence in extirpated larval firefly lanterns. 2. Transmitter and synephrine show many similarities of action. They are as follows: (a) They both act directly on the lantern. (b) Their response latencies are relatively constant. (c) Both stimulate ATP production. (d) Neither induces a persistent intermediate in anoxic lanterns. (e) No monoamine oxidase enzyme appears to act on them. (f) The luminescence-inducing action of both is rapidly blocked by chlorpromazine. (g) They show identical responses in the presence of dichloroisoproterenol. 3. Luminescence induced by transmitter is much more rapidly extinguished than that induced by syneprine. 4. The possible reasons for the difference in luminescence extinction rate between the two agents are discussed and their different modes of delivery are emphasized.

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