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Edith Hemaspaandra

Publications and source records attributed to Edith Hemaspaandra.

At least 55 records · Page 3Linked to original sources
arXiv2008

How Hard Is Bribery in Elections?

We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by a certain amount of bribing voters a specified candidate can be made the election's winner? We study this problem for election systems as varied as scoring protocols and Dodgson voting, and in a variety of settings regarding homogeneous-vs.-nonhomogeneous electorate bribability, bounded-size-vs.-arbitrary-sized candidate sets, weighted-vs.-unweighted voters, and succinct-vs.-nonsuccinct input specification. We obtain both polynomial-time bribery algorithms and proofs of the intractability of bribery, and indeed our results show that the complexity of bribery is extremely sensitive to the setting. For example, we find settings in which bribery is NP-complete but manipulation (by voters) is in P, and we find settings in which bribing weighted voters is NP-complete but bribing voters with individual bribe thresholds is in P. For the broad class of elections (including plurality, Borda, k-approval, and veto) known as scoring protocols, we prove a dichotomy result for bribery of weighted voters: We find a simple-to-evaluate condition that classifies every case as either NP-complete or in P.

cs.GT↗
arXiv2008

Generalized Modal Satisfiability

It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits. We consider both the uni-modal and the multi-modal case, and study the dual problem of validity as well.

cs.CC↗
arXiv2008

On the Complexity of Elementary Modal Logics

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide class of relevant logics: Many important subclasses of modal logics can be obtained by restricting the allowed models with first-order Horn formulas. We show that the satisfiability problem for each of these logics is either NP-complete or PSPACE-hard, and exhibit a simple classification criterion. Further, we prove matching PSPACE upper bounds for many of the PSPACE-hard logics.

cs.CC↗
arXiv2007

Copeland Voting Fully Resists Constructive Control

Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Faliszewski et al. [FHHR07] proved that Llull voting (which is here denoted by Copeland^1) and a variant (here denoted by Copeland^0) of Copeland voting are computationally resistant to many, yet not all, types of constructive control and that they also provide broad resistance to bribery. We study a parameterized version of Copeland voting, denoted by Copeland^alpha where the parameter alpha is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates in Copeland elections. We establish resistance or vulnerability results, in every previously studied control scenario, for Copeland^alpha, for each rational alpha, 0 <alpha < 1. In particular, we prove that Copeland^0.5, the system commonly referred to as ``Copeland voting,'' provides full resistance to constructive control. Among the systems with a polynomial-time winner problem, this is the first natural election system proven to have full resistance to constructive control. Results on bribery and fixed-parameter tractability of bounded-case control proven for Copeland^0 and Copeland^1 in [FHHR07] are extended to Copeland^alpha for each rational alpha, 0 < alpha < 1; we also give results in more flexible models such as microbribery and extended control.

cs.GT↗
arXiv2005

The Complexity of Poor Man's Logic

Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the complexity of the satisfiability problem for K dropped from PSPACE-complete to coNP-complete (Schmidt-Schauss and Smolka, 1991 and Donini et al., 1992). In this paper we show that not all modal logics behave like K. In particular, we show that the complexity of the satisfiability problem with respect to frames in which each world has at least one successor drops from PSPACE-complete to P, but that in contrast the satisfiability problem with respect to the class of frames in which each world has at most two successors remains PSPACE-complete. As a corollary of the latter result, we also solve the open problem from Donini et al.'s complexity classification of description logics (Donini et al., 1997). In the last section, we classify the complexity of the satisfiability problem for K for all other restrictions on the set of operators.

cs.LO↗
arXiv2005

The Complexity of Kings

A king in a directed graph is a node from which each node in the graph can be reached via paths of length at most two. There is a broad literature on tournaments (completely oriented digraphs), and it has been known for more than half a century that all tournaments have at least one king [Lan53]. Recently, kings have proven useful in theoretical computer science, in particular in the study of the complexity of the semifeasible sets [HNP98,HT05] and in the study of the complexity of reachability problems [Tan01,NT02]. In this paper, we study the complexity of recognizing kings. For each succinctly specified family of tournaments, the king problem is known to belong to $Π_2^p$ [HOZZ]. We prove that this bound is optimal: We construct a succinctly specified tournament family whose king problem is $Π_2^p$-complete. It follows easily from our proof approach that the problem of testing kingship in succinctly specified graphs (which need not be tournaments) is $Π_2^p$-complete. We also obtain $Π_2^p$-completeness results for k-kings in succinctly specified j-partite tournaments, $k,j \geq 2$, and we generalize our main construction to show that $Π_2^p$-completeness holds for testing k-kingship in succinctly specified families of tournaments for all $k \geq 2$.

cs.CC↗
arXiv2005

Isomorphic Implication

We study the isomorphic implication problem for Boolean constraints. We show that this is a natural analog of the subgraph isomorphism problem. We prove that, depending on the set of constraints, this problem is in P, NP-complete, or NP-hard, coNP-hard, and in parallel access to NP. We show how to extend the NP-hardness and coNP-hardness to hardness for parallel access to NP for some cases, and conjecture that this can be done in all cases.

cs.CC↗
arXiv2005

Dichotomy for Voting Systems

Scoring protocols are a broad class of voting systems. Each is defined by a vector $(α_1,α_2,...,α_m)$, $α_1 \geq α_2 \geq >... \geq α_m$, of integers such that each voter contributes $α_1$ points to his/her first choice, $α_2$ points to his/her second choice, and so on, and any candidate receiving the most points is a winner. What is it about scoring-protocol election systems that makes some have the desirable property of being NP-complete to manipulate, while others can be manipulated in polynomial time? We find the complete, dichotomizing answer: Diversity of dislike. Every scoring-protocol election system having two or more point values assigned to candidates other than the favorite--i.e., having $||\{α_i \condition 2 \leq i \leq m\}||\geq 2$--is NP-complete to manipulate. Every other scoring-protocol election system can be manipulated in polynomial time. In effect, we show that--other than trivial systems (where all candidates alway tie), plurality voting, and plurality voting's transparently disguised translations--\emph{every} scoring-protocol election system is NP-complete to manipulate.

cs.GT↗
arXiv2005

Recognizing When Heuristics Can Approximate Minimum Vertex Covers Is Complete for Parallel Access to NP

For both the edge deletion heuristic and the maximum-degree greedy heuristic, we study the problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r, where r is a fixed rational number. Our main results are that these problems are complete for the class of problems solvable via parallel access to NP. To achieve these main results, we also show that the restriction of the vertex cover problem to those graphs for which either of these heuristics can find an optimal solution remains NP-hard.

cs.CC↗
arXiv2004

All Superlinear Inverse Schemes are coNP-Hard

How hard is it to invert NP-problems? We show that all superlinearly certified inverses of NP problems are coNP-hard. To do so, we develop a novel proof technique that builds diagonalizations against certificates directly into a circuit.

cs.CC↗
arXiv2004

Complexity Results in Graph Reconstruction

We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts $c \geq 1$ of deletion: 1) $GI \equiv^{l}_{iso} VDC_{c}$, $GI \equiv^{l}_{iso} EDC_{c}$, $GI \leq^{l}_{m} LVD_c$, and $GI \equiv^{p}_{iso} LED_c$. 2) For all $k \geq 2$, $GI \equiv^{p}_{iso} k-VDC_c$ and $GI \equiv^{p}_{iso} k-EDC_c$. 3) For all $k \geq 2$, $GI \leq^{l}_{m} k-LVD_c$. 4)$GI \equiv^{p}_{iso} 2-LVC_c$. 5) For all $k \geq 2$, $GI \equiv^{p}_{iso} k-LED_c$. For many of these results, even the $c = 1$ case was not previously known. Similar to the definition of reconstruction numbers $vrn_{\exists}(G)$ [HP85] and $ern_{\exists}(G)$ (see page 120 of [LS03]), we introduce two new graph parameters, $vrn_{\forall}(G)$ and $ern_{\forall}(G)$, and give an example of a family $\{G_n\}_{n \geq 4}$ of graphs on $n$ vertices for which $vrn_{\exists}(G_n) < vrn_{\forall}(G_n)$. For every $k \geq 2$ and $n \geq 1$, we show that there exists a collection of $k$ graphs on $(2^{k-1}+1)n+k$ vertices with $2^{n}$ 1-vertex-preimages, i.e., one has families of graph collections whose number of 1-vertex-preimages is huge relative to the size of the graphs involved.

cs.CC↗
arXiv2004

Dichotomy Theorems for Alternation-Bounded Quantified Boolean Formulas

In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NP-complete, and gave a simple criterion to determine which of the two cases holds. This result is surprising in light of Ladner's theorem, which implies that there are an infinite number of complexity classes between P and NP-complete (under the assumption that P is not equal to NP). Schaefer also stated a dichotomy theorem for quantified generalized Boolean formulas, but this theorem was only recently proven by Creignou, Khanna, and Sudan, and independently by Dalmau: Determining truth of quantified Boolean formulas is either PSPACE-complete or in P. This paper looks at alternation-bounded quantified generalized Boolean formulas. In their unrestricted forms, these problems are the canonical problems complete for the levels of the polynomial hierarchy. In this paper, we prove dichotomy theorems for alternation-bounded quantified generalized Boolean formulas, by showing that these problems are either $Σ_i^p$-complete or in P, and we give a simple criterion to determine which of the two cases holds. This is the first result that obtains dichotomy for an infinite number of classes at once.

cs.CC↗
arXiv2004

The Complexity of Boolean Constraint Isomorphism

In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems (nowadays usually called Boolean constraint satisfaction problems) and showed that all these satisfiability problems are either in P or NP-complete. In recent years, similar results have been obtained for quite a few other problems for Boolean constraints.Almost all of these problems are variations of the satisfiability problem. In this paper, we address a problem that is not a variation of satisfiability, namely, the isomorphism problem for Boolean constraints. Previous work by Böhler et al. showed that the isomorphism problem is either coNP-hard or reducible to the graph isomorphism problem (a problem that is in NP, but not known to be NP-hard), thus distinguishing a hard case and an easier case. However, they did not classify which cases are truly easy, i.e., in P. This paper accomplishes exactly that. It shows that Boolean constraint isomorphism is coNP-hard (and GI-hard), or equivalent to graph isomorphism, or in P, and it gives simple criteria to determine which case holds.

cs.CC↗
arXiv2003

Complexity of Cycle Length Modularity Problems in Graphs

The even cycle problem for both undirected and directed graphs has been the topic of intense research in the last decade. In this paper, we study the computational complexity of \emph{cycle length modularity problems}. Roughly speaking, in a cycle length modularity problem, given an input (undirected or directed) graph, one has to determine whether the graph has a cycle $C$ of a specific length (or one of several different lengths), modulo a fixed integer. We denote the two families (one for undirected graphs and one for directed graphs) of problems by $(S,m)\hbox{-}{\rm UC}$ and $(S,m)\hbox{-}{\rm DC}$, where $m \in \mathcal{N}$ and $S \subseteq \{0,1, ..., m-1\}$. $(S,m)\hbox{-}{\rm UC}$ (respectively, $(S,m)\hbox{-}{\rm DC}$) is defined as follows: Given an undirected (respectively, directed) graph $G$, is there a cycle in $G$ whose length, modulo $m$, is a member of $S$? In this paper, we fully classify (i.e., as either polynomial-time solvable or as ${\rm NP}$-complete) each problem $(S,m)\hbox{-}{\rm UC}$ such that $0 \in S$ and each problem $(S,m)\hbox{-}{\rm DC}$ such that $0 \notin S$. We also give a sufficient condition on $S$ and $m$ for the following problem to be polynomial-time computable: $(S,m)\hbox{-}{\rm UC}$ such that $0 \notin S$.

cs.CC↗
arXiv2001

Using the No-Search Easy-Hard Technique for Downward Collapse

The top part of the preceding figure [figure appears in actual paper] shows some classes from the (truth-table) bounded-query and boolean hierarchies. It is well-known that if either of these hierarchies collapses at a given level, then all higher levels of that hierarchy collapse to that same level. This is a standard ``upward translation of equality'' that has been known for over a decade. The issue of whether these hierarchies can translate equality {\em downwards\/} has proven vastly more challenging. In particular, with regard to the figure above, consider the following claim: $$P_{m-tt}^{Σ_k^p} = P_{m+1-tt}^{Σ_k^p} \implies DIFF_m(Σ_k^p) coDIFF_m(Σ_k^p) = BH(Σ_k^p). (*) $$ This claim, if true, says that equality translates downwards between levels of the bounded-query hierarchy and the boolean hierarchy levels that (before the fact) are immediately below them. Until recently, it was not known whether (*) {\em ever\/} held, except for the degenerate cases $m=0$ and $k=0$. Then Hemaspaandra, Hemaspaandra, and Hempel \cite{hem-hem-hem:j:downward-translation} proved that (*) holds for all $m$, for $k > 2$. Buhrman and Fortnow~\cite{buh-for:j:two-queries} then showed that, when $k=2$, (*) holds for the case $m = 1$. In this paper, we prove that for the case $k=2$, (*) holds for all values of $m$. Since there is an oracle relative to which ``for $k=1$, (*) holds for all $m$'' fails \cite{buh-for:j:two-queries}, our achievement of the $k=2$ case cannot to be strengthened to $k=1$ by any relativizable proof technique. The new downward translation we obtain also tightens the collapse in the polynomial hierarchy implied by a collapse in the bounded-query hierarchy of the second level of the polynomial hierarchy.

cs.CC↗
arXiv2000

Almost-Everywhere Superiority for Quantum Computing

Simon as extended by Brassard and Høyer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine almost everywhere.

quant-ph↗
arXiv1999

Query Order and the Polynomial Hierarchy

Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. The present paper studies, for the first time, query order as it applies to the levels of the polynomial hierarchy. We prove that the levels of the polynomial hierarchy are order-oblivious. Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. We prove that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P.

cs.CC↗