arXiv subjects

Edith Hemaspaandra

Publications and source records attributed to Edith Hemaspaandra.

At least 19 recordsLinked to original sources

arXiv2025

On the Parallelizability of Approval-Based Committee Rules

Approval-Based Committee (ABC) rules are an important tool for choosing a fair set of candidates when given the preferences of a collection of voters. Though finding a winning committee for many ABC rules is NP-hard, natural variations for these rules with polynomial-time algorithms exist. The recently introduced Method of Equal Shares, an important ABC rule with desirable properties, is also computable in polynomial time. However, when working with very large elections, polynomial time is not enough and parallelization may be necessary. We show that computing a winning committee using these polynomial-time ABC rules (including the Method of Equal Shares) is P-hard, thus showing they cannot be parallelized. In contrast, we show that finding a winning committee can be parallelized when the votes are single-peaked or single-crossing for the important ABC rule Chamberlin-Courant.

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arXiv2023

Complexity of Conformant Election Manipulation

It is important to study how strategic agents can affect the outcome of an election. There has been a long line of research in the computational study of elections on the complexity of manipulative actions such as manipulation and bribery. These problems model scenarios such as voters casting strategic votes and agents campaigning for voters to change their votes to make a desired candidate win. A common assumption is that the preferences of the voters follow the structure of a domain restriction such as single peakedness, and so manipulators only consider votes that also satisfy this restriction. We introduce the model where the preferences of the voters define their own restriction and strategic actions must ``conform'' by using only these votes. In this model, the election after manipulation will retain common domain restrictions. We explore the computational complexity of conformant manipulative actions and we discuss how conformant manipulative actions relate to other manipulative actions.

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arXiv2023

The Complexity of $(P_k, P_\ell)$-Arrowing

For fixed nonnegative integers $k$ and $\ell$, the $(P_k, P_\ell)$-Arrowing problem asks whether a given graph, $G$, has a red/blue coloring of $E(G)$ such that there are no red copies of $P_k$ and no blue copies of $P_\ell$. The problem is trivial when $\max(k,\ell) \leq 3$, but has been shown to be coNP-complete when $k = \ell = 4$. In this work, we show that the problem remains coNP-complete for all pairs of $k$ and $\ell$, except $(3,4)$, and when $\max(k,\ell) \leq 3$. Our result is only the second hardness result for $(F,H)$-Arrowing for an infinite family of graphs and the first for 1-connected graphs. Previous hardness results for $(F, H)$-Arrowing depended on constructing graphs that avoided the creation of too many copies of $F$ and $H$, allowing easier analysis of the reduction. This is clearly unavoidable with paths and thus requires a more careful approach. We define and prove the existence of special graphs that we refer to as ``transmitters.'' Using transmitters, we construct gadgets for three distinct cases: 1) $k = 3$ and $\ell \geq 5$, 2) $\ell > k \geq 4$, and 3) $\ell = k \geq 4$. For $(P_3, P_4)$-Arrowing we show a polynomial-time algorithm by reducing the problem to 2SAT, thus successfully categorizing the complexity of all $(P_k, P_\ell)$-Arrowing problems.

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arXiv2023

Using Weighted Matching to Solve 2-Approval/Veto Control and Bribery

Determining the complexity of election attack problems is a major research direction in the computational study of voting problems. The paper "Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters" by Erd\'elyi et al. (JAAMAS 2021) provides a comprehensive study of the complexity of control problems. The sole open problem is constructive control by replacing voters for 2-Approval. We show that this case is in P, strengthening the recent RP (randomized polynomial-time) upper bound due to Fitzsimmons and Hemaspaandra (IJCAI 2022). We show this by transforming 2-Approval CCRV to weighted matching. We also use this approach to show that priced bribery for 2-Veto elections is in P. With this result, and the accompanying (unsurprising) result that priced bribery for 3-Veto elections is NP-complete, this settles the complexity for $k$-Approval and $k$-Veto standard control and bribery cases.

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arXiv2022

Insight into Voting Problem Complexity Using Randomized Classes

The first step in classifying the complexity of an NP problem is typically showing the problem in P or NP-complete. This has been a successful first step for many problems, including voting problems. However, in this paper we show that this may not always be the best first step. We consider the problem of constructive control by replacing voters (CCRV) introduced by Loreggia et al. (2015) for the scoring rule First-Last, which is defined by $\langle 1, 0, \dots, 0, -1\rangle$. We show that this problem is equivalent to Exact Perfect Bipartite Matching, and so CCRV for First-Last can be determined in random polynomial time. So on the one hand, if CCRV for First-Last is NP-complete then RP = NP, which is extremely unlikely. On the other hand, showing that CCRV for First-Last is in P would also show that Exact Perfect Bipartite Matching is in P, which would solve a well-studied 40-year-old open problem. By considering RP as an option we also gain insight into the complexity of CCRV for 2-Approval, ultimately showing it in P, which settles the complexity of the sole open problem in the comprehensive table from Erd\'{e}lyi et al. (2021).

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arXiv2021

Kemeny Consensus Complexity

The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition.

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arXiv2020

Effective Feedback for Introductory CS Theory: A JFLAP Extension and Student Persistence

Computing theory analyzes abstract computational models to rigorously study the computational difficulty of various problems. Introductory computing theory can be challenging for undergraduate students, and the main goal of our research is to help students learn these computational models. The most common pedagogical tool for interacting with these models is the Java Formal Languages and Automata Package (JFLAP). We developed a JFLAP server extension, which accepts homework submissions from students, evaluates the submission as correct or incorrect, and provides a witness string when the submission is incorrect. Our extension currently provides witness feedback for deterministic finite automata, nondeterministic finite automata, regular expressions, context-free grammars, and pushdown automata. In Fall 2019, we ran a preliminary investigation on two sections (Control and Study) of the required undergraduate course Introduction to Computer Science Theory. The Study section used our extension for five targeted homework questions, and the Control section solved and submitted these problems using traditional means. Our results show that on these five questions, the Study section performed better on average than the Control section. Moreover, the Study section persisted in submitting attempts until correct, and from this finding, our preliminary conclusion is that minimal (not detailed or grade-based) witness feedback helps students to truly learn the concepts. We describe the results that support this conclusion as well as a related hypothesis conjecturing that with witness feedback and unlimited number of submissions, partial credit is both unnecessary and ineffective.

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arXiv2019

Complexity of Stability

Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the chromatic number of a graph (i.e., the smallest number of colors needed to color all vertices such that no two adjacent vertices are of the same color) can be applied in solving practical tasks as diverse as pattern matching, scheduling jobs to machines, allocating registers in compiler optimization, and even solving Sudoku puzzles. Typically, however, the underlying graphs are subject to (often minor) changes. To make these applications of graph parameters robust, it is important to know which graphs are stable for them in the sense that adding or deleting single edges or vertices does not change them. We initiate the study of stability of graphs for such parameters in terms of their computational complexity. We show that, for various central graph parameters, the problem of determining whether or not a given graph is stable is complete for \Theta_2^p, a well-known complexity class in the second level of the polynomial hierarchy, which is also known as "parallel access to NP."

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arXiv2019

The Complexity of Online Bribery in Sequential Elections (Extended Abstract)

Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all voters' votes. But neither of those assumptions always holds. In many real-world settings, votes come in sequentially, and the briber may have a use-it-or-lose-it moment to decide whether to bribe/alter a given vote, and at the time of making that decision, the briber may not know what votes remaining voters are planning on casting. In this paper, we introduce a model for, and initiate the study of, bribery in such an online, sequential setting. We show that even for election systems whose winner-determination problem is polynomial-time computable, an online, sequential setting may vastly increase the complexity of bribery, in fact jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. On the other hand, we show that for some natural, important election systems, such a dramatic complexity increase does not occur, and we pinpoint the complexity of their bribery problems in the online, sequential setting.

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arXiv2019

Finding Optimal Solutions With Neighborly Help

Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal colorings for all one-edge-deleted subgraphs? Studying such questions not only gives detailed insight into the structure of the problem itself, but also into the complexity of related problems; most notably graph theory's core notion of critical graphs (e.g., graphs whose chromatic number decreases under deletion of an arbitrary edge) and the complexity-theoretic notion of minimality problems (also called criticality problems, e.g., recognizing graphs that become 3-colorable when an arbitrary edge is deleted). We focus on two prototypical graph problems, Colorability and Vertex Cover. For example, we show that it is NP-hard to compute an optimal coloring for a graph from optimal colorings for all its one-vertex-deleted subgraphs, and that this remains true even when optimal solutions for all one-edge-deleted subgraphs are given. In contrast, computing an optimal coloring from all (or even just two) one-edge-added supergraphs is in P. We observe that Vertex Cover exhibits a remarkably different behavior, demonstrating the power of our model to delineate problems from each other more precisely on a structural level. Moreover, we provide a number of new complexity results for minimality and criticality problems. For example, we prove that Minimal-3-UnColorability is complete for DP (differences of NP sets), which was previously known only for the more amenable case of deleting vertices rather than edges. For Vertex Cover, we show that recognizing beta-vertex-critical graphs is complete for Theta_2^p (parallel access to NP), obtaining the first completeness result for a criticality problem for this class.

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arXiv2019

The Complexity of Online Bribery in Sequential Elections

Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all votes. However, in many real-world settings votes come in sequentially, and the briber may have a use-it-or-lose-it moment to decide whether to alter a given vote, and when making that decision the briber may not know what votes remaining voters will cast. We introduce a model for, and initiate the study of, bribery in such an online, sequential setting. We show that even for election systems whose winner-determination problem is polynomial-time computable, an online, sequential setting may vastly increase the complexity of bribery, jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. But we also show that for some natural, important election systems, such a dramatic complexity increase does not occur, and we pinpoint the complexity of their bribery problems.

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arXiv2018

Very Hard Electoral Control Problems

It is important to understand how the outcome of an election can be modified by an agent with control over the structure of the election. Electoral control has been studied for many election systems, but for all studied systems the winner problem is in P, and so control is in NP. There are election systems, such as Kemeny, that have many desirable properties, but whose winner problems are not in NP. Thus for such systems control is not in NP, and in fact we show that it is typically complete for $\Sigma_2^p$ (i.e., ${\rm NP}^{\rm NP}$, the second level of the polynomial hierarchy). This is a very high level of complexity. Approaches that perform quite well for solving NP problems do not necessarily work for $\Sigma_2^p$-complete problems. However, answer set programming is suited to express problems in $\Sigma_2^p$, and we present an encoding for Kemeny control.

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arXiv2018

Election Score Can Be Harder Than Winner

Election systems based on scores generally determine the winner by computing the score of each candidate and the winner is the candidate with the best score. It would be natural to expect that computing the winner of an election is at least as hard as computing the score of a candidate. We show that this is not always the case. In particular, we show that for Young elections for dichotomous preferences the winner problem is easy, while determining the score of a candidate is hard. This complexity behavior has not been seen before and is unusual. The easiness of the winner problem for dichotomous Young crucially uses the fact that dichotomous preferences guarantee the transitivity of the majority relation. In addition to dichotomous preferences we also look at single-peaked preferences, the most well-studied domain restriction that guarantees the transitivity of the majority relation. We show that for the three major hard election systems and their natural variants, dichotomous Young is the only case where winner is easy and score is hard. This also solves an open question from Lackner and Peters (AAAI 2017), by providing a polynomial-time algorithm for Dodgson score for single-peaked electorates.

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arXiv2017

The Robustness of LWPP and WPP, with an Application to Graph Reconstruction

We show that the counting class LWPP [FFK94] remains unchanged even if one allows a polynomial number of gap values rather than one. On the other hand, we show that it is impossible to improve this from polynomially many gap values to a superpolynomial number of gap values by relativizable proof techniques. The first of these results implies that the Legitimate Deck Problem (from the study of graph reconstruction) is in LWPP (and thus low for PP, i.e., $\rm PP^{\mbox{Legitimate Deck}} = PP$) if the weakened version of the Reconstruction Conjecture holds in which the number of nonisomorphic preimages is assumed merely to be polynomially bounded. This strengthens the 1992 result of K\"{o}bler, Sch\"{o}ning, and Tor\'{a}n [KST92] that the Legitimate Deck Problem is in LWPP if the Reconstruction Conjecture holds, and provides strengthened evidence that the Legitimate Deck Problem is not NP-hard. We additionally show on the one hand that our main LWPP robustness result also holds for WPP, and also holds even when one allows both the rejection- and acceptance- gap-value targets to simultaneously be polynomial-sized lists; yet on the other hand, we show that for the #P-based analog of LWPP the behavior much differs in that, in some relativized worlds, even two target values already yield a richer class than one value does. Despite that nonrobustness result for a #P-based class, we show that the #P-based "exact counting" class $\rm C_{=}P$ remains unchanged even if one allows a polynomial number of target values for the number of accepting paths of the machine.

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arXiv2017

Credimus

We believe that economic design and computational complexity---while already important to each other---should become even more important to each other with each passing year. But for that to happen, experts in on the one hand such areas as social choice, economics, and political science and on the other hand computational complexity will have to better understand each other's worldviews. This article, written by two complexity theorists who also work in computational social choice theory, focuses on one direction of that process by presenting a brief overview of how most computational complexity theorists view the world. Although our immediate motivation is to make the lens through which complexity theorists see the world be better understood by those in the social sciences, we also feel that even within computer science it is very important for nontheoreticians to understand how theoreticians think, just as it is equally important within computer science for theoreticians to understand how nontheoreticians think.

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arXiv2016

High-Multiplicity Election Problems

The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the electorate and their counts, i.e., high-multiplicity representation. We consider how this representation affects the complexity of election problems. High-multiplicity representation may be exponentially smaller than standard representation, and so many polynomial-time algorithms for election problems in standard representation become exponential-time. Surprisingly, for polynomial-time election problems, we are often able to either adapt the same approach or provide new algorithms to show that these problems remain polynomial-time in the high-multiplicity case; this is in sharp contrast to the case where each voter has a weight, where the complexity usually increases. In the process we explore the relationship between high-multiplicity scheduling and manipulation of high-multiplicity elections. And we show that for any fixed set of job lengths, high-multiplicity scheduling on uniform parallel machines is in P, which was previously known for only two job lengths. We did not find any natural case where a polynomial-time election problem does not remain in P when moving to high-multiplicity representation. However, we found one natural NP-hard election problem where the complexity does increase, namely winner determination for Kemeny elections.

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arXiv2016

Modeling Single-Peakedness for Votes with Ties

Single-peakedness is one of the most important and well-known domain restrictions on preferences. The computational study of single-peaked electorates has largely been restricted to elections with tie-free votes, and recent work that studies the computational complexity of manipulative attacks for single-peaked elections for votes with ties has been restricted to nonstandard models of single-peaked preferences for top orders. We study the computational complexity of manipulation for votes with ties for the standard model of single-peaked preferences and for single-plateaued preferences. We show that these models avoid the anomalous complexity behavior exhibited by the other models. We also state a surprising result on the relation between the societal axis and the complexity of manipulation for single-peaked preferences.

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arXiv2016

The Complexity of Controlling Candidate-Sequential Elections

Candidate control of elections is the study of how adding or removing candidates can affect the outcome. However, the traditional study of the complexity of candidate control is in the model in which all candidates and votes are known up front. This paper develops a model for studying online control for elections where the structure is sequential with respect to the candidates, and in which the decision regarding adding and deleting must be irrevocably made at the moment the candidate is presented. We show that great complexity---PSPACE-completeness---can occur in this setting, but we also provide within this setting polynomial-time algorithms for the most important of election systems, plurality.

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