Efficient Algorithms for Online Decision Problems

2003 ◽  
pp. 26-40 ◽  
Author(s):  
Adam Kalai ◽  
Santosh Vempala
Keyword(s):  
Efficient Algorithms ◽  
Decision Problems

scholarly journals Efficient algorithms for online decision problems

2005 ◽  
Vol 71 (3) ◽  
pp. 291-307 ◽  
Author(s):  
Adam Kalai ◽  
Santosh Vempala
Keyword(s):  
Efficient Algorithms ◽  
Decision Problems

scholarly journals Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

2020 ◽  
Vol 69 ◽  
pp. 109-141
Author(s):  
Paul Goldberg ◽  
Alexandros Hollender ◽  
Warut Suksompong
Keyword(s):  
Approximation Algorithms ◽  
Efficient Algorithms ◽  
Decision Problems ◽  
Fair Allocation ◽  
Prior Work ◽  
Cake Cutting ◽  
Np Hardness

We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results extending and strengthening those from prior work. Finally, we investigate connections between approximate and exact envy-freeness, as well as between continuous and discrete cake cutting.

scholarly journals Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

2020 ◽  
Vol 34 (02) ◽  
pp. 1990-1997
Author(s):  
Paul W. Goldberg ◽  
Alexandros Hollender ◽  
Warut Suksompong
Keyword(s):  
Approximation Algorithms ◽  
Efficient Algorithms ◽  
Decision Problems ◽  
Fair Allocation ◽  
Prior Work ◽  
Cake Cutting ◽  
Np Hardness

We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results strengthening those from prior work.

Tidal Flow: A Fast and Teachable Maximum Flow Algorithm

2018 ◽  
Vol 12 ◽  
pp. 25-41
Author(s):  
Matthew C. FONTAINE
Keyword(s):  
Computer Science ◽  
Tidal Flow ◽  
Maximum Flow ◽  
Efficient Algorithms ◽  
Science Students ◽  
Flow Algorithm ◽  
Maximum Flows

Among the most interesting problems in competitive programming involve maximum flows. However, efficient algorithms for solving these problems are often difficult for students to understand at an intuitive level. One reason for this difficulty may be a lack of suitable metaphors relating these algorithms to concepts that the students already understand. This paper introduces a novel maximum flow algorithm, Tidal Flow, that is designed to be intuitive to undergraduate andpre-university computer science students.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

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