Orthology analysis is an important part of data analysis in many areas of bioinformatics such as comparative genomics and molecular phylogenetics. The ever-increasing flood of sequence data, and hence the rapidly increasing number of genomes that can be compared simultaneously, calls for efficient software tools as brute-force approaches with quadratic memory requirements become infeasible in practise. The rapid pace at which new data become available, furthermore, makes it desirable to compute genome-wide orthology relations for a given dataset rather than relying on relations listed in databases. The program Proteinortho described here is a stand-alone tool that is geared towards large datasets and makes use of distributed computing techniques when run on multi-core hardware. It implements an extended version of the reciprocal best alignment heuristic. We apply Proteinortho to compute orthologous proteins in the complete set of all 717 eubacterial genomes available at NCBI at the beginning of 2009. We identified thirty proteins present in 99% of all bacterial proteomes. Proteinortho significantly reduces the required amount of memory for orthology analysis compared to existing tools, allowing such computations to be performed on off-the-shelf hardware.

/pdf/proteinortho-detection-of-co-orthologs-in-large-scale-1sdb6vw560.pdf

Proteinortho : Detection of (Co-)orthologs in large-scale analysis

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

/pdf/handbook-of-computational-social-choice-12i1xbv1b8.pdf

Handbook of Computational Social Choice

We consider approval-based committee voting, i.e., the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. We then check if this axiom is fulfilled by well-known approval-based voting rules. We show that the answer is negative for most of the rules we consider, with notable exceptions of PAV (Proportional Approval Voting), an extreme version of RAV (Reweighted Approval Voting), and, for a restricted preference domain, MAV (Minimax Approval Voting). We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR, while other rules do not. We also consider several other questions related to JR and EJR, including the relationship between JR/EJR and unanimity, and the complexity of the associated algorithmic problems.

/pdf/justified-representation-in-approval-based-committee-voting-5anu6ay1hv.pdf

Justified representation in approval-based committee voting

We consider approval-based committee voting, i.e. the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. However, it turns out that several prominent approval-based voting rules may fail to output such a committee. In particular, while Proportional Approval Voting (PAV) always outputs a committee that provides JR, Reweighted Approval Voting (RAV), a tractable approximation to PAV, does not have this property. We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR, while other rules we consider do not; indeed, EJR can be used to characterize PAV within the class of weighted PAV rules. We also consider several other questions related to JR and EJR, including the relationship between JR/EJR and core stability, and the complexity of the associated algorithmic problems.

Justified Representation in Approval-Based Committee Voting

A committee selection rule (or, multiwinner voting rule) is a mapping that takes a collection of strict preference rankings and a positive integer k as input, and outputs one or more subsets of candidates of size k. In this paper we consider committee selection rules that can be viewed as generalizations of single-winner scoring rules, including SNTV, Bloc, k-Borda, STV, as well as several variants of the Chamberlin–Courant rule and the Monroe rule and their approximations. We identify two natural broad classes of committee selection rules, and show that many of the existing rules belong to one or both of these classes. We then formulate a number of desirable properties of committee selection rules, and evaluate the rules we consider with respect to these properties.

/pdf/properties-of-multiwinner-voting-rules-yfy7pxhq9d.pdf

Properties of multiwinner voting rules.

A one-to-one correspondence between colorings and stable sets

Solving vertex coloring problems as maximum weight stable set problems

https://cris.unibo.it/bitstream/11585/713744/4/VKS_full.pdf

The vertex k-cut problem

Chromatic characterization of biclique covers

Solving Vertex Coloring Problems as Maximum Weighted Stable Set Problems.

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