Most people believe that the principal weaknesses of vampires are sunlight, wooden stakes in inconvenient places, and extortionate dentist bills. Most people are mistaken. Being creatures of undeniably aristocratic persuasion, vampires fear social humiliation above all. In particular, exhibiting symptoms of haematological indigestion (typically induced by an incompatible blood type) constitutes a social death sentence, occasionally followed by the literal kind. To preserve gastric decorum within the undead community, we study the Ghoul Exchange Programme, an online matching market in which vampires trade ghouls so as to align blood types. We model it as a stochastic matching problem, prove that no policy can stabilise it under a natural symmetry condition on arrivals (called mirror invariance), and analyse two ways to recover stability: admitting human volunteers, or tolerating a bounded discard rate. Both yield a trade-off between delay and waste. Our framework maps onto Kidney Exchange Programmes: volunteers become deceased donors, discard becomes wait-list mortality, and any reward-maximising policy is revealed to carry an implicit valuation of patient outcomes, with consequences ranging from the inequitable to the disturbing.
We study control and bribery problems for stable matchings: a central authority (the controller, resp., briber) may add agents, delete agents, delete acceptable pairs, swap two adjacent agents in some agent’s preference list, or arbitrarily reorder some agent’s preference list, in an instance of Stable Marriage or Stable Roommates. We extend previous work on control and bribery in stable matchings by Boehmer et al. [8]. We consider goals capturing individual and pair inclusion, stability, and uniqueness requirements: matching a designated agent ( ), matching a designated pair ( ), realizing a stable matching consistent with a given matching ( ), making a given matching the unique stable matching ( ), or guaranteeing that a stable (resp., perfect and stable) matching exists ( ∃ / ∃ ). We provide a unified complexity map for all non-trivial action–goal combinations in both settings, consolidating known results and extending the study to the roommates model, where stable matchings need not exist.
We study temporal fair division with indivisible goods that arrive sequentially and must be allocated irrevocably. In contrast to the usual online model, we assume that valuations and future arrivals are known in advance, and ask how unfairness evolves during the process. We introduce cumulative maximum envy: the sum, over all rounds, of the maximum pairwise envy at that round. Equivalently, this is the area under the worst-envy curve, and it captures both the magnitude and the duration of envy. For a fixed arrival order, we show that the corresponding decision problem is strongly NP-complete and that minimizing this objective admits no constant-factor approximation unless P = NP, even under identical valuations and even under binary valuations. We complement these hardness results with a dynamic program that gives pseudopolynomial-time solvability for a constant number of agents, polynomial-time algorithms in further restricted settings, and an FPTAS for fixed n under identical integer valuations. We then study a sequencing variant where the algorithm may choose the arrival order. This variant remains NP-complete even for two agents with identical valuations; however, a simple greedy algorithm achieves a 3/2-approximation for n=2 agents, an n/(n-1)-approximation for any number of agents, and an additive guarantee depending on the maximum value of any good.
We study the problem of allocating indivisible chores with additive costs, seeking allocations that are weighted envy-free up to one chore (WEF1) and fractionally Pareto optimal (fPO). Mahara (SODA 2026) recently proved that such allocations always exist, but finding one in polynomial time for general instances remains open. We give a polynomial-time algorithm for the setting with bounded surplus chores: for every fixed constant s, a WEF1 and fPO allocation can be computed whenever the number of chores is at most the number of agents plus s. This guarantee allows for arbitrarily many agents and arbitrarily many distinct cost functions. Our approach works through a prescribed bundle size problem. The key parameter is the number of chores assigned beyond the first chore in each nonempty bundle. When this surplus is S, we decide whether there is a WEF1 and fPO allocation respecting the prescribed bundle sizes, and compute one if it exists, in time m^S poly(n,m,L) , where L is the total input bit length. The algorithm relies on two structural observations: with positive costs and fixed bundle sizes, fPO is equivalent to minimizing the product of assigned costs; and agents who receive at most one chore impose no nontrivial WEF1 constraints. We complement the algorithm with a hardness result showing that the prescribed bundle size problem becomes strongly NP-hard when the surplus is unbounded, even with two agent types and bundle sizes restricted to {3,5} .
We study constrained coalition formation in games induced by friends, enemies, and neutrals, under the two standard refinements of additively separable preferences: friend-oriented and enemy-oriented. We ask for partitions that are individually rational (IR), while additionally requiring exactly k non-empty coalitions, each satisfying a prescribed lower and upper bound on its size. Although IR alone is trivial to satisfy for any hedonic game, the size constraints make it computationally intractable to decide whether a feasible partition exists. The two models tell strikingly different stories. Under enemy-oriented preferences, the problem collapses to size-constrained graph coloring, and its complexity follows accordingly. Under friend-oriented preferences, however, the picture is far more intricate, and is governed by the enmity structure rather than the friendships. The complexity is further shaped by two factors: how strict the imposed size requirements are, and whether relationships are symmetric or asymmetric, with several cases turning out tractable in the symmetric setting but intractable once asymmetry is allowed. Charting this boundary in terms of both classical and parameterized complexity, we provide a complete understanding of which properties of the friend/enemy structure are responsible for hardness.
